A particle moves a distance \(x\) in time \(t\) according to equation \(x = (t+5)^{-1}\). The acceleration of the particle is proportional to:
1. | \((\text{velocity})^{\frac{3}{2}}\) | 2. | \((\text{distance})^2\) |
3. | \((\text{distance})^{-2}\) | 4. | \((\text{velocity})^{\frac{2}{3}}\) |
A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:
1. B
2. C
3. D
4. A
A particle moves in a straight line, according to the law \(x=4a[t+a\sin(t/a)], \) where \(x\) is its position in metres, \(t\) is in seconds & \(a\) is some constant, then the velocity is zero at:
1. | \(x = 4 a^2\pi\) metres | 2. | \(t = \pi\) sec |
3. | \(t =0\) sec | 4. | none of the above |
A point moves in a straight line so that its displacement is x m at time t sec, given by . Its acceleration in at time 1 sec is:
1.
2.
3.
4.
The position x of a particle moving along the x-axis varies with time t as x = , where x is in meters and t is in seconds. The particle reverses its direction of motion at:
1. x = 40 m
2. x = 10 m
3. x = 20 m
4. x = 30 m
Assertion (A): | Displacement of a body may be zero when distance travelled by it is not zero. |
Reason (R): | The displacement is the longest distance between initial and final position. |
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. |
Two cars A and B are travelling in the same direction with velocities v1 and v2 . When the car A is at a distance d behind car B, the driver of the car A applied the brake producing uniform retardation a. There will be no collision when-
1.
2.
3.
4.
Which of the following four statements is false?
1. | A body can have zero velocity and still be accelerated. |
2. | A body can have a constant velocity and still have a varying speed. |
3. | A body can have a constant speed and still have a varying velocity. |
4. | The direction of the velocity of a body can change when its acceleration is constant. |
The initial velocity of a particle is u (at t = 0) and the acceleration f is given by at. Which of the following relation is valid?
1.
2.
3.
4. v = u
A stone falls freely from rest from a height h and it travels a distance of in the last second. The value of h is:
1. | 145 m | 2. | 100 m |
3. | 122.5 m | 4. | 200 ms |