Numericals of Motion in One Dimension

Motion in One Dimension

MUTIPLE CHOICE QUESTION:
1. The length of a second hand in watch is 1 cm. The change in velocity of its tips in 15 s is
a) Zero              b) π/30√2 cm/s              c) π/30 cm/s                             d) π√2/30 cm/s

2. A particle moving along a straight line travels half of its distance with uniform speed 30 m/s and the remaining half of the distance with the speed 60 m/s. The average speed of the particle is
a) 45 m/s          b) 42 m/s                         c) 40 m/s                                   d) 50 m/s

3. A boat is moving with a velocity (3i + 4j) with respect to ground. The water in the river is moving with a velocity (-3i – 4j) with respect to ground. The relative velocity of boat with respect to water is
a) 8j                     b) -6i – 8j                      c) 6i + 8j                                    d) zero

4. During the first 18 min of a 60 min trip, a car has an average speed of 11 m/s. What should be the average speed fore remaining 42 min so that car is having an average speed of 21 m/s for the entire trip?
a) 25.3 m/s        b) 29.2 m/s                   c) 31 m/s                                    d) 35.6 m/s

5. A particle moves along a straight line. Its position at any instant is given by x = 32t – 8t3/3 where x is in meter and t is in second. Find the acceleration of the particle at the instant when the particle is at rest.
a) -16 m/s2       b) -32 m/s2                   c) 32 m/s2                                  d) 16 m/s2

6. A particle is moving along x-axis whose position is varying with the time according to the relation
X = -3t + t3 where x is in meter and t is in second. The displacement of particle for t = 1s to t = 3s is
a) + 16m           b) -16 m                            c) +20 m                                    d) -20 m

7. A particle moves in the x=y plane with the velocity vx =8t – 2 and vy=2. If it passes through the point x = 14 and y = 4 at t = 2 s, the equation of the path is
a) x = y2 – y + 2             b) x = y2 – 2            c) x = y2 + y -6                 d) None of these

8. The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = (8t – 5t2) meter and x =6t meter where t is in second. The velocity of projection is
a) 8 m/s            b) 6 m/s                            c) 10 m/s                                  d) data insufficient

9. The horizontal and vertical displacement of a particle moving along a curved line are given by x = 5t and y = 2t2 + t. Time after which its velocity vector makes an angle of 45˚ with the horizontal is
a) 0.5 s                b) 1 s                                  c) 2 s                                          d) 1.5 s

10. A ball is released from the top of a tower of height h meter. Its takes T second to reach the ground. What is the position of the ball in T/3 second?
a) h/9 meter from the ground                            b) (7h/9) meter from the ground
c) (8h/9) meter from the ground                      d) (17h/9) meter from the ground

11. Two objects are moving along the same straight line. They cross a point A with an acceleration a, 2a and velocity 2u, u at time t= 0. The distance moved by the object when one overtakes the other is
a) 6u2/a                  b) 2u2/a                     c) 4u2/a                               d) 8u2/a

12. Water drops fall at regular interval from a tap 5 m above the ground. The third drop is leaving the tap, the instant the first drop touches the ground. How far above the ground is the second drop at that instant (g =10 m/s2)
a) 1.25 m                 b) 2.50 m                  c) 3.75 m                               d) 4.00 m

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