The motion of a particle along a straight line is described by the equation
\(x=8+12 t-t^3\)
where \(x\) is in metre and t is in second. The retardation of the particle when its velocity becomes zero is:
1. | \(24 ~\text{ms}^{-2} \) | 2. | zero |
3. | \( 6 ~\text{ms}^{-2} \) | 4. | \(12 ~\text{ms}^{-2} \) |
A boy standing at the top of a tower of \(20\) m height drops a stone. Assuming \(g=10\) m/s2, the velocity with which it hits the ground will be:
1. \(20\) m/s
2. \(40\) m/s
3. \(5\) m/s
4. \(10\) m/s
A particle is projected upwards. The times corresponding to height h while ascending and while descending are t1 and t2 respectively. The velocity of projection will be:
1. gt1
2. gt2
3.
4.
Four marbles are dropped from the top of a tower one after the other at a one-second interval. The first one reaches the ground after 4 seconds. When the first one reaches the ground the distances between the first and second, the second and third, and the third and fourth will be, respectively:
1. | 35 m, 25 m, and 15 m | 2. | 30 m, 20 m, and 10 m |
3. | 20 m, 10 m, and 5 m | 4. | 40 m, 30 m, and 20 m |
The acceleration of a particle starting from rest varies with time according to the relation A = – aω2sinωt. The displacement of this particle at a time t will be:
1.
2.
3.
4.
Given below are two statements:
Assertion (A): | Position-time graph of a stationary object is a straight line parallel to the time axis. |
Reason (R): | For a stationary object, the position does not change with time. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |
Acceleration-time graph of a body is shown.
The corresponding velocity-time graph of the same body is:
1. | 2. | ||
3. | 4. |
Which of the following velocity-time graphs shows a realistic situation for a body in motion?
1. | 2. | ||
3. | 4. |
Which graph represents a uniformly accelerated motion?
1. | 2. | ||
3. | 4. |
In the following graph, the distance travelled by the body in metres is:
1. | \(200\) | 2. | \(250\) |
3. | \(300\) | 4. | \(400\) |