Motion in a Straight Line · Question 36

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

Two bodies A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is

1. 4/5
2. 5/4
3. 12/5
4. 5/12

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t - t3. How long would the particle travel before coming to rest ?

1. 16 m
2. 24 m
3. 40 m
4. 56 m

A ball is thrown vertically upward. It has a speed of 10 m/s when it has reached one half of its maximum height. How high does the ball rise? (Take g = 10 m/s2.)

1. 10 m
2. 5 m
3. 15 m
4. 20 m

The displacement x of a particle varies with time t as x = ae- t + be t, where a, b, and are positive constants. The velocity of the particle will

1. be independent of
2. drop to zero when =
3. go on decreasing with time
4. go on increasing with time.

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time ? (Given g = 9.8 m/s2)

1. more than 19.6 m/s
2. at least 9.8 m/s
3. any speed less than 19.6 m/s
4. only with speed 19.6 m/s.

If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is

1. ut
2. 12gt2
3. ut - 12gt2
4. (u + gt)t.

A particle is thrown vertically upward. Its velocity at half of the height is 10 m/s, then the maximum height attained by it is (g = 10 m/s2)

1. 8 m
2. 20 m
3. 10 m
4. 16 m

Motion of a particle is given by equation s = (3t3 + 7t2 + 14t + 8) m. The value of acceleration of the particle at t = 1 s is

1. 10 m/s2
2. 32 m/s2
3. 23 m/s2
4. 16 m/s2