Sunday, 18 February 2018

Numericals of Motion in One Dimension

Motion in One Dimension

1. A particle is moving with a velocity of v= (3+6t+9t2) cm/s. Find out
a) The acceleration of the particle at t=3 s.
b) The displacement of the particle between t=5 s to t= 8 s.

2. The motion of the particle along a straight line is described by the function x= (2t-3)2 where x is in meter and t is in seconds.
a) Find the position, velocity and acceleration of the particle at t=2sec.
b) Find velocity of the particle at origin.

3. A man crosses a river in a boa. If he crosses the river in minimum time he takes 10 min with a drift 120 m. If he crosses the river taking shortest path, he takes 12.5 min, find:
a) Width of the river
b) Velocity of the boat with respect to water.
c) Speed of the current.

4. A rocket is fired vertically upwards from the ground with a resultant vertical acceleration of 10 m/s2. The fuel is finished in 1 min and it continues to move up.
a) What is the maximum height reached?
b) After how much time from then will the maximum height be reached? (Take g = 10 m/s2)

5. Velocity of a particle moving in a straight line varies with its displacement as v= ( 4+4𝑠) m/s. Displacement of the particle at time t=0 is s=0. Find displacement of the particle at t=2 sec.

6. A particle is moving in a straight line with constant acceleration. If x, y and z be the distance described by the particle during the pth, qth and rth second respectively, prove that
(q-r) x+ (r-p) y+ (p-q) z = 0

7. To test the quality of a tennis ball, you drop it into the floor from a height of 4 m. It rebounds to a height of 2 m. If the ball is in contact to the floor for 12 ms, what is the average acceleration of the ball during the contact? Take g=9.8 m/s2.

8. A particle moves along a straight path and its velocity depends on time as v=3t-t2. Here v is in m/s and t in second. Find:
a) Average velocity
b) Average speed for first five seconds.

9. A man wishes to cross a river of width 120 m by a motorboat. His rowing speed in still water is 3 m/s and his maximum walking speed is 1 m/s. The river flows with velocity of 4 m/s.
a) Find the path which he should follow to get to the point directly opposite to his starting point in the shortest time.
b) Also, find the time which he takes to reach his destination.

PASSAGE: Q. NO. 10 to 13
An elevator without a ceiling is ascending up with an acceleration of 5 ms-2. A boy on the elevator shoots a ball in vertical upward direction from a height of 2 m above the floor of elevator. At this instant the elevator is moving upwards with a velocity of 10 m/s, and the floor of the elevator is at a height of 50 m from the ground. The initial speed of the ball is 15 m/s with respect to the elevator. Consider the duration for which the ball strikes the floor of the elevator in answering following questions. (g=10 ms-2).

10. The time in which the ball strikes the floor of the elevator is given by
a) 2.13 sec                   b) 2.0 sec                        c) 1.0 sec                   d) 3.12 sec

11. The maximum height reached by the ball, as measured from the ground would be
a) 73.65 m                  b) 116.25 m                      c) 82.56 m                d) 63.25 m

12. Displacement of the ball with respect to the ground during its flight would be
a) 16.25 m                    b) 8.76 m                         c) 20.24 m               d) 30.56 m

13. The maximum separation between the floor of elevator and the ball during its flight would be

a) 12 m                         b) 15 m                             c) 9.5 m                    d) 7.5 m


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