# Velocity and Time

Srivastava’s

Srivastava’s

MOTION IN ONE DIMENSION

1.

A particle is projected vertically upwards with a velocity 20 m s1 from the top of the tower of height 100 m. Determine the time it takes to reach the ground. Answer: t 2 1 6 sec.

A particle is dropped from the top of the tower of height h. At the same instant another particle is projected vertically upwards from the bottom of the tower with such a velocity that it will be able to just reach the top of the tower. When and at what height from ground the two particles meet?

3h

h

Answer: t

and x

2g

4

2.

3.

4.

5.

A car covers first half of the total journey with uniform velocity 40 m s1 and the other half of the journey with uniform velocity 60 m s1. Find its average velocity in the entire journey.

Answer: 48 m s1

A cyclist moves from A to B with uniform speed v0. While returning from B to A it travels for half the time with uniform speed v1 and for the other half the time with uniform speed v2. Find the average speed of the cyclist for the complete journey. 2v 0 v 1 v 2

Answer: v

2v 0 v 1 v 2

Front end of a uniformly accelerated train crosses a telegraph post with velocity u. Its rear end crosses the same post with velocity v. Find the velocity with which mid point of the train crosses the same post.

u2 v2

2

6. The engine of a boat moving with velocity v0 is switched off. Due to resistance of water it experiences a deceleration whose magnitude is directly proportional to instantaneous velocity given by a kv , where k is a constant. Find the distance it covers before it stops.

v

Answer: s 0

k

7. Two stones are projected vertically up wards one after the other with same velocities 20 m s1 with a time interval of 2 sec. After what time and at what height from point of projection do they meet?

Answer: t 1 and s 15 m.

th

8. A particle dropped from the top of a tower, covers 9

of the total height in its

25

last second of journey. Find the height of the tower.

Answer: h 125 m.

9. A balloon starts rising upwards from rest with uniform acceleration 4 m s2. 5 sec after the start a stone is dropped from it. What time will the stone take to reach ground?

Answer: 2 14 sec.

10. A balloon starts moving upwards with a uniform acceleration 2 m s2. 10 sec after the start of journey a stone is dropped from it. 12 sec after the start of journey another stone is dropped. Find the distance between two stones 14 sec after the start of journey.

Answer: 72 m.

Answer:

MARATHON-11

94

Motion in One Dimension

11. Two cars A and B approach each other with same speed v = 36 km hr1. When distance between them is 200 m a bird starts off from car A to car B with a uniform speed 72 km hr1, on reaching car B it immediately turns back and moves towards car A with same speed. The bird keeps moving between the two cars to and fro till they collide. Find the total distance traveled by the bird and the number of trips made by the bird between the cars.

Answer: 200 m., infinite

12. As a motorcyclist moving with uniform velocity 20 m s1 passes a stationary car the car starts off with uniform acceleration of 2 m s2. What distance ahead the point of start the car will overtake the motorcyclist?

Answer: 400 m.

13. A car starts moving from rest with uniform acceleration 2 m s2 at the same instant a motorcyclist 36 m behind the car is also moving in the same direction with uniform velocity 20 m s1. For how long the motorcyclist will remain ahead of the car? Also find the maximum distance it can be ahead of the car and at what time. Answer: t 16 sec, 64 m at t = 10 sec.

14. The x-coordinate of a particle moving on the x-axis is given by x 24t 3t 2 , where x is in meter and t in seconds. Find

i) the initial velocity and acceleration of the particle.

ii) the maximum x-coordinate the particle can reach.

Answer: i) 24 m s1 ii) xmax 48 m

15. A uniformly...

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