## Problem 1

- the particle is continuously moving in positive x direction
- the particle is at rest
- the velocity increases up to a time t
_{0}and then becomes constant - the particle moves at a constant velocity up to time t
_{0}, and then stops

## Problem 2

_{a}, and x

_{b}be the magnitude of displacements in the first 10 seconds and the next 10 seconds, respectively, then,

- x
_{a}< x_{b} - x
_{a}= x_{b} - x
_{a}> x_{b} - the information is insufficient to decide the relation of x
_{a}with x_{b}

## Problem 3

- a upward
- ( g - a ) upward
- ( g - a ) downward
- g downward

## Problem 4

_{a}, and the ball B hits the ground with a speed v

_{b}. We have

- v
_{a}> v_{b} - v
_{a}= v_{b} - v
_{a}< v_{b} - the relation between v
_{a}and v_{b}depends on height of the building above the ground.

## Problem 5

- is always perpendicular to the acceleration
- is never perpendicular to the acceleration
- is perpendicular to the acceleration for one instant only
- is perpendicular to the acceleration for two instants.

## Problem 6

- the faster one
- the slower one
- both will reach simultaneously
- depends on the masses.

## Problem 7

^{o}for the projectile A and 45

^{o}for the projectile B. If R

_{a}and R

_{b}be the horizontal range for the two projectiles respectively, then :

- R
_{a}< R_{b} - R
_{a}= R_{b} - R
_{a}> R_{b} - the information is insufficient to decide the relation
of R
_{a}with R_{b}

## Problem 8

- the displacement is zero
- the distance covered is zero
- the average speed is zero
- the average velocity is zero

## Problem 9

- Average speed of a particle in a given time is never less than the magnitude of the average velocity.
- It is possible to have a situation in which $\left | \frac{\overrightarrow{dv}}{dt} \right | \neq 0$ but $\frac{d}{dt}\left | \overrightarrow{v}\right | = 0 $
- The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in that interval.
- 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.

## Problem 10

- varying speed without having varying velocity.
- varying velocity without having varying speed.
- nonzero acceleration without having varying velocity.
- nonzero acceleration without having varying speed.

## Problem 11

- If the velocity and acceleration have opposite sign, the object is slowing down.
- If the position and velocity have opposite sign, the particle is moving towards the origin.
- If the velocity is zero at an instant, the acceleration should also be zero at that instant.
- If the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval.

## Problem 12

- The acceleration at t = 0 must be zero.
- The acceleration at t = 0 may be zero.
- If the acceleration is zero from t = 0 to t = 10 s, the speed is also zero in this interval.
- If the speed is zero from t = 0 to t = 10 s the acceleration is also zero in this interval.

## Problem 13

- The magnitude of the velocity of a particle is equal to its speed.
- The magnitude of average velocity in an interval is equal to its average speed in that interval.
- It is possible to have a situation in which the speed of a particle is always zero but the average speed is not zero.
- It is possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero.

## Problem 14

- The particle has a constant acceleration.
- The particle has never turned around.
- The particle has zero displacement.
- 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.

## Problem 15

- The particle has come to rest 6 times.
- The maximum speed is at t = 6 s.
- The velocity remains positive for t = 0 to t = 6 s.
- The average velocity for the total period shown is negative.

## Problem 16

^{2}.

- The frames must be at rest with respect to each other.
- The frames may be moving with respect to each other but neither should be accelerated with respect to the other.
- The acceleration of S2 with respect to S1 may either be zero or 8 m/s
^{2}. - The acceleration of S2 with respect to S1 may be anything between zero and 8 m/s
^{2}

## Problem 17

- a railway carriage moving without jerks between two stations.
- a monkey sitting on top of a man cycling smoothly on a circular track.
- a spinning cricket ball that turns sharply on hitting the ground.
- a tumbling beaker that has slipped off the edge of a table.

## Problem 18

- A lives closer to school than B.
- A starts from the school earlier than B.
- A walks faster than B.
- A reaches home earlier than B reaches his home.

## Problem 19

- the particle may have zero speed at a moment, with non-zero acceleration at that moment.
- the particle may have zero speed and non-zero velocity at a moment.
- if the particle is moving with constant speed, then it must have zero acceleration. (considering infinite acceleration impossible)
- if the particle has positive value of acceleration, then it must be speeding up.

## Problem 20

## Problem 21

Answers

1 - d) | 2 - d) | 3 - d) | 4 - b) | 5 - c) |

6 - c) | 7 - d) | 8 - a), d) | 9 - a), b), c) | 10 - b), d) |

11 - a), b), d) | 12 - b), c), d) | 13 - a) | 14 - a), d) | 15 - a) |

16 - d) | 17 - a), b) | 18 - a), b) | 19 - a), c) | 20 - a), b), c), d) |

21 - a) |