 ##### Introduction

This video $$x^{2+a}$$ introduces us to the concept of motion in one direction; assuming that the objects in motion are non-deformable and will act as particle whose every part have the same motion.

##### Position

This video explains the meaning of position of an object, which is always defined with respect to a reference point. It also explains the sign of position based on the choice of convention followed in determining them.

##### Dist Disp - I

This video explains the definition and difference between distance and displacement. Distance is defined as total length of the path covered while displacement is the difference between initial and final position.

##### Dist Disp - II

It explains the independence of sign of displacement from the sign of initial and final position. Displacement can increase or decrease, however distance will always increase

##### Speed

This video explains concept of speed in terms of distance covered per unit time. It also explains the concept of average and instantaneous speed

##### Velocity

This video explains the concept of velocity and how it is different from speed in the terms of direction and displacement?

##### Q1

Two children start at one end of a street, the origin, run to the other end, then head back. On the way back A is ahead of B. Which statement is correct about the distances run and the displacements from the origin?
(a) A has run a greater distance and his displacement is greater than Bs
(b) B has run a greater distance and his displacement is greater than As
(c) A has run a greater distance, but his displacement is less than Bs
(d) B has run a greater distance, but his displacement is less than As

##### Q2

Mark the correct statement :
Is the magnitude of instantaneous velocity equal to speed ?
Is the magnitude of average velocity equal to average speed ?
Is it possible to have a situation in which the speed of a particle is always zero but the average speed is not zero ?
Is it possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero ?

##### Acceleration

This video explains the concept of uniform motion, acceleration as a vector quantity, deceleration and their relationship with direction of velocity in terms of speeding up or slowing down.

##### Q3

Which is/ are correct?
a) If velocity of a body changes, it must have some acceleration
b) If speed of a body changes, it must have some acceleration
c) If body has acceleration, its speed must change
d) If body has acceleration, its speed may change

##### Q4

Find the relationship between change in acceleration with respect to change in velocity and speed.
Which is/ are correct?
a) If velocity of a body changes, it must have some acceleration
b) If speed of a body changes, it must have some acceleration
c) If body has acceleration, its speed must change
d) If body has acceleration, its speed may change

##### Q5

At t = 0, a particle moving along x axis is at position xo = -20 m. The signs of the particles initial velocity vo (at time to) and constant acceleration a are, respectively, for four situations: (1) +, + (2) +, - (3) -, + (4) -, - . In which situations will the particle
(a) stop momentarily
(b) pass through the origin
(c) never pass through the origin ?

##### Q6

Mark the correct statements for a particle going on a straight line:
a) If the velocity and acceleration have opposite sign, the object is slowing down
b) If the position and velocity have opposite signs, the particle is moving towards the origin
c) If the velocity is zero at an instant, the acceleration should also be zero at that instant
d) If the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval

##### Q7

Average acceleration is in the direction of
(a) initial velocity
(b) final velocity
(c) change in velocity
(d) final velocity if initial velocity is zero

##### Q8

Pick the correct statements:
(a) Is Average speed of a particle in a given time is never less than the magnitude of the average velocity?
(b) It is possible to have a situation in which the average velocity of a particle is zero in a time interval.
(c) It is possible then the instantaneous velocity is never zero in the interval
(d) The average velocity of a particle moving on a straight line is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval.

##### Q9

A particle confined to move along the x axis, moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5 s time interval. Velocity of the particle at x = 8.0 m is 2.8 m/s. What is the acceleration during this time interval?

##### Graphs - 1

This video explains the way to find the average velocity, instantaneous velocity and acceleration from a position-time graph of a moving particle with help of slope measurement and its relation to the derivative of the graph function.

##### Q10

The position of an object at equal time intervals is shown in figure. Which graph below correctly represents position versus time for this object?

##### Q11

The displacement time graph of a moving particle is shown in Figure. The instantaneous velocity of the particle is negative at the point

##### Q12

Figure shows the position of a particle moving along x-axis as a function of time.
a) The particle has come to rest 6 times
b) The maximum speed is at t = 6s
c) The velocity remains positive for t = 0 to t = 6s
d) The average velocity for the total period shown is negative

##### Q13

Find the point(s) on the graph where
(a) Instantaneous velocity is equal to the average velocity
(b) Instantaneous speed is equal to the magnitude of average velocity
(c) Instantaneous speed is equal to the average speed
(d) Will average speed be equal to the magnitude of average velocity. ?

##### Graphs - 2

This video explains the method of plotting velocity-time graph and then acceleration-time graph from a given position-time graph of an object.

##### Q14

Velocity - time plot for a particle moving on a straight line is given.
(a) The particle has a constant acceleration ?
(b) The particle has never turned around ?
(c) The particle has zero displacement ?
(d) The average speed in the interval 0 to 10 s is the same as the average speed in the interval 10 s to 20 s ?

##### Q15

Displacement - time graph of a body is shown in figure.
Velocity - time graph of the motion of the body will be

##### Q16

The graph in figure shows the velocity versus time graph for a ball. Which explanation best fits the motion of the ball as shown by the graph?
(a) The ball is falling, is caught, and is thrown down with greater velocity
(b) The ball is rolling, stops, and then continues rolling
(c) The ball is rising, hits the ceiling, and falls down
(d) The ball is falling, hits the floor, and bounces up

##### Graphs - 3

This video explains the method of plotting displacement-time graph from a given velocity time graph. And velocity-time graph from a given acceleration-time graph for a body. It also explains the displacement as the area under the velocity-time graph and velocity as the area under the acceleration-time graph respectively.

##### Q17

The velocity time graph of a body is shown in the figure. The displacement covered by the body in 8 s is

##### Q18

The acceleration versus time graph of a particle is shown in the figure. The respective v-t graphs of the particle is

##### Equations

This video shows the derivation of equation of motion involving initial velocity, final velocity, displacement, time and acceleration. These are most important equations of the motion.

##### Acc due to Gravity

This video demonstrates the very well-known example of motion with constant acceleration i.e the free falling motion of a body moving under acceleration due to gravity.

##### Q19

A ball is dropped from a tower. It takes 4 second to reach bottom of tower.
a) Find the velocity of the ball at the bottom of tower.
b) Find the height of the tower.
Take g = 10 m/s2

##### Q20

A ball is thrown up with velocity 30 m/s. Find
a) Time taken to reach the maximum height.
b) Maximum height reached by the ball.
Take g = 10 m/s2

##### Q21

A ball is thrown with velocity = 30 m/s from a tower of height 80 m. Find the velocity of the ball as it hits the ground and the time taken if
a) Ball is thrown upwards
b) Ball is thrown downwards
Take g = 10 m/s2

##### Q22

Two particles A and B are thrown from the top of a tower with the same speed. A is thrown straight up and B is thrown straight down. They hit the ground with speeds vA and vB respectively.

Is vA = vB ?

##### Q23

A juggler throws two balls to the same height so that one is at the halfway point going up when the other is at the half way point coming down. At that point:
(a) Their velocities and accelerations are equal
(b) Their velocities are equal but their accelerations are equal and opposite
(c) Their accelerations are equal but their velocities are equal and opposite
(d) Their velocities and accelerations are both equal and opposite

##### Q24

A particle is thrown directly upward past three evenly spaced windows of equal heights. Rank the windows according to
(a) average speed of the particle
(b) the time taken
(c)magnitude of acceleration
(d) the change in velocity while passing them

##### 1

A velocity vs position graph is plotted for a particle moving along positive x-axis with constant acceleration. The velocity of particle at the origin will be???

##### 2

A ball is thrown vertically upwards. It was observed at a height h twice with a time interval Dt. The initial velocity of the ball is

##### 3

A graph is plotted between the square of the velocity of a particle and the distance moved by the particle. The acceleration of the particle is???

##### 4

If a particle takes t second less and acquires a velocity of v m/s more in falling through the same distance on two planets where the accelerations due to gravity are 2g and 8g respectively then find the velocity?..

##### 5

A body is projected vertically upwards. If t1 and t2 be the times at which it is at a height h above the point of projection while ascending and descending respectively, then find h in terms of t1 and t2

##### 6

A body falls freely under gravity. The distance travelled by it in the last second of its journey equals the distance travelled by it in the first three second of its free fall. Find the total time taken by the body to reach the ground.

##### 7

Water drops fall at regular intervals from a roof. At an instant when a drop is about to leave the roof, the separations between 3 successive drops below the roof are in the ratio in increasing order will be?..?

##### 8

A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is 4 cm and that of iron plate is 2 cm. A bullet fired goes through the wood first and then penetrates 1cm into iron. A similar bullet fired with the same velocity from opposite direction goes through iron first and then penetrates 2 cm into wood. If a1 and a2 be the retardations offered to the bullet by wood and iron plates respectively then find the relation between a1 and a2 ?

##### 9

A bullet loses 1/20 of its velocity in passing through a plank. The least number of the planks required to stop the bullet is?..?

##### 10

A particle moves in a straight line with a velocity v(t) = t - 4 m/s where t is time in seconds. The distance covered by the particle in 8s is ??

##### 11

At t = 0, a particle is located at x = 25 m and has a velocity of 15 m/s in the positive x direction. The acceleration of the particle varies with time as shown in diagram. What is the position of the particle at t = 5.0 s?
(a) 175 m
(b) 125 m
(c) 138 m
(d) 204 m

##### 12

Find the final position of a particle when
a particle starts from rest at x = 0 and moves in positive X-direction for 10s with a positive acceleration and for the next 20 s with a negative acceleration.

##### 13

A balloon starts rising from the ground with a known acceleration. After sometime, a stone is released from the balloon. Find the distance covered, displacement, total time taken to reach the ground. Also state whether the stone begins to move down just after being released.

##### 14

An object is thrown vertically upwards and has an upward velocity of 18 m/s when it reached one fourth of its maximum height above its launch point. What is the initial (launch) speed of the object?

##### 15

The velocity at the midway point on the vertical path of a ball able to reach a maximum height y when thrown vertically upward with initial velocity vi is:

##### 16

Two bicycle riders A and B start from rest at the bottom of a long straight road with constant upward slope. A can only accelerate at three quarters (3/4th) of the acceleration of B. If B takes 5.0 min to reach the top, how much earlier should A start to reach the top at the same time as B?

##### 17

Athlete A runs beside Athlete B for half the required distance. A runs the remaining distance at his regular speed and arrives 90 s ahead of B. What is the ratio of As regular speed to Bs speed after half of the distance? Total time taken by B is given?.

##### 18

Plotted are the velocities as functions of time for two cars A and B. A is moving with constant velocity. Driver of the car B starts her car at the instant A passes her. At what instants in the time are drivers A and B side by side?

##### 19

Two bodies of masses m1 and m2 are dropped from heights h1 and h2 respectively. They reach the ground after time t1 and t2 and strike the ground with v1 and v2, respectively. Find the ratio t1/t2 and v1/v2 in terms of h1 and h2

##### 20

At time t = 0, object 1 is dropped from a height h and after 1 second, object 2 is thrown down from the same height. Object 2 reaches the ground 1/4th of a second later than object 1 as shown in graph of vertical positions y versus time t during the falling, until both objects have hit the ground. With approximately what speed is object 2 thrown down?

##### 21

An object falls a distance h from rest. If it travels 0.50h in the last 1.00 s, find the time and height of its fall. Also explain the physically unacceptable solution of the quadratic equation in t that obtained in the solution.

##### 22

A ball is dropped from a buildings roof and passes a window, taking 0.125 s to fall from the top of the window to the bottom of the window, a distance of 1.20 m. It then falls to a sidewalk and bounces back. The time the ball spends below the bottom of the window is 2.00 s. Assuming that the upward flight is an exact reverse of the fall, how tall is the building?

##### 23

A speedy tortoise can run with a known velocity of and a rabbit can run 20 times as fast. In a race of certain length, they both start at the same time, but the rabbit stops to rest some given time. The tortoise wins by a certain distance. What was the length of the race?

##### 24

A particle moving in a straight line covers half the distance with a speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speeds of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is ?.?

##### 25

A particle starts from rest with a given acceleration which varies with time as shown in the figure. The maximum speed of the particle will be??

##### 26

A car accelerates from rest at a constant rate ?a? for sometime after which it decelerates at a constant rate ?b? to come to rest. If the total time lapse is t, find a) the maximum velocity attained and (b) the total distance travelled.

##### 27

The position of a particle moving along the x axis is given by
X(t) = 6.0t2 - 1.0t3, where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?

##### 28

The velocity of a particle moving along the x axis is given for t > 0 by v(x) = (32.0 t2 - 2.00 t3) m/s, where t is in sec. What is the acceleration of the particle when (after t = 0) it achieves its maximum displacement in the positive x direction?

##### 29

A particle initially (t = 0) moving with a velocity u is subjected to a retarding force, as a result of which it decelerates at a rate a = - k?v, here v is the instantaneous velocity and k is a positive constant. The time T taken by the particle to come to rest will be??

##### 30

Given is graph of the variation of velocity (v) of a body with position (x) from the origin O. Plot the variation of the acceleration
(a) with position (x) by deriving the equation with use of differentiation.

##### 31

The velocity (v) of a body moving along the positive x-direction varies with displacement (x) from the origin as v = k?x, where k is a constant. Plot the displacement-time (x-t) graph of the motion of the body?

##### 32

The displacement x of a particle varies with time according to the relation x = (1-e-bt). Then which of the following is true
a) At t = 1/b, the displacement of the particle is nearly (2/3)(a/b)
b) The velocity and acceleration of the particle at t = 0 are ?a? and ?- ab? respectively.
(c) The particle cannot reach a point at a distance x from its starting position if x > a/b.
(d) The particle will come back to its starting point as t ??.

##### 33

A particle moving in a straight line is subjected to a constant retardation ?a? which varies with instantaneous velocity v as a = -kv, where k is a positive constant. If the initial velocity of the particle is ?u? at t = 0, then which of the following is true.
(a) The velocity at time t is given by v = u ? at.
(b) The velocity decreases exponentially with time.
(c) The velocity will decrease to u/2 in time 1/k.
(d) The total distance covered by the particle before coming to rest is u/k.

##### 34

The displacement x of a particle moving in one dimension, is related to time t by the equation t = ?x + 3 where x is in meters and t in seconds. Find the displacement of the particle when its velocity is zero.

##### 35

The motion of a body is given by the equation dv/dt = 6 ? 3v
Where v is the velocity (in m/s) at time t (in seconds). The body is rest at t = 0. Then which of the following is true.
(a) The velocity of the body when its acceleration is zero is 2m/s (b) The initial acceleration of the body is 6 m/s2.
(c) The velocity of body when the acceleration is half the initial value is 1 m/s.
(d) The body has a uniform acceleration