## QUESTIONS

- If a particle is accelerating, it is either speeding up or speeding down. Do you agree with this statement?
- Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed. Do you agree with this statement?
- Is the vertical height taken by a long jumper important while taking the jump?
- A woman standing on the edge of a cliff throws a ball straight up with a speed of 8 km/h and then throws another ball straight down with a speed of 8 km/h from the same position. What is the ratio of the speeds with which the balls hit the ground ?
- Find the average velocity during the time of flight, if a particle is projected with v at an angle θ with horizontal plane.
- Establish the relation x(t) = v(0)t + (1/2) at^2 by calculus method.
- Derive the velocity–time relationship by (i) calculus method, (ii) graphical method.
- A stone is thrown upwards from the top of a tower 85 m high. It reaches the ground in 5 second. Calculate (i) the greatest height above the ground, (ii) the velocity with which it reaches the ground and (iii) the time taken to reach the maximum height. (Given: g = 10 m/s^2.)
- A car starts from rest and accelerates uniformly for 10 s to a velocity of 8 m/s. It then runs at a constant velocity and is finally brought to rest in 64 m with a constant retardation. The total distance covered by the car is 584 m. Find the values of acceleration, retardation and total time taken.
- Prove that there are two times for which a projectile travels the same vertical distance. Also prove that the sum of the two times is equal to the time of flight.

## ANSWERS

- No, not always. In case of uniform circular motion, the particle is accelerating but its speed is

neither decreasing nor increasing, only direction of velocity changes. - This is true as motion under gravity is independent of mass of the body and so the body comes

back to the point of projection with the same speed. - Yes, because for the longest jump the player should throw himself at an angle of 45 degree wrt horizontal. The vertical height required for this purpose should be

u2/4g, where u is velocity of throw. If the vertical height is different from u2/4g then the angle will be different from 45 degree and the horizontal distance covered also will be less. - 1 : 1, both the balls will hit the ground with the same speed.
- v cosθ

8. h = 3.2 m, v = 42 m/s, t = 0.8 sec.

9. 0.8 m/s2, 0.5 m/s2 and 86 sec.