Motion in a Straight Line · Question 40

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