Motion in a Straight Line · Question 27

A particle moves a distance x in time t according to equation x = (t + 5)-1. The acceleration of particle is proportional to

1. (velocity)3/2
2. (distance)2
3. (distance)-2
4. (velocity)2/3

A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18 s. What is the value of v? (Take g = 10 m/s2)

1. 75 m/s
2. 55 m/s
3. 40 m/s
4. 60 m/s

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S1 and that covered in the first 20 seconds is S2, then

1. S2 = 3S1
2. S2 = 4S1
3. S2 = S1
4. S2 = 2S1

A bus is moving with a speed of 10 m s-1 on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

1. 40 m s-1
2. 25 m s-1
3. 10 m s-1
4. 20 m s-1

A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 m s-1 to 20 m s-1 while passing through a distance 135 m in t second. The value of t is

1. 12
2. 9
3. 10
4. 1.8

The distance travelled by a particle starting from rest and moving with an acceleration 43 m s-2, in the third second is

1. 103 m
2. 193 m
3. 6 m
4. 4 m

A particle shows distance - time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point [figure]

1. D
2. A
3. B
4. C

A particle moving along x-axis has acceleration f, at time t, given by f = f0 (1 - tT ), where f0 and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle's velocity (vx) is

1. 12f0T2
2. f0T2
3. 12f0T
4. f0T

A car moves from X to Y with a uniform speed vu and returns to X with a uniform speed vd. The average speed for this round trip is

1. vu vd
2. vd vuvd + vu
3. vu + vd2
4. 2vd vuvd + vu

The position x of a particle with respect to time t along x-axis is given by x = 9t2 - t3 where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the +x direction?

1. 54 m
2. 81 m
3. 24 m
4. 32 m