Q. No.A stone falls freely from rest from a height \(h\) and it travels a distance of \(\frac{9 h}{25}\) in the last second. The value of \(h\) is:
1.
\(145\) m
2.
\(100\) m
3.
\(122.5\) m
4.
\(200\) ms
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. \(v = u + a t^{2}\)
2. \(v = u + a \frac{t^{2}}{2}\)
3. \(v = u + a t\)
4. \(v= u\)
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. |
Two cars \(A\) and \(B\) are travelling in the same direction with velocities \(v_1\) and \(v_2\) \((v_1>v_2).\) When the car \(A\) is at a distance \(d\) behind the car \(B,\) the driver of the car \(A\) applied the brake producing uniform retardation \(a.\) There will be no collision when:
1. \(d < \frac{\left( v_{1} - v_{2} \right)^{2}}{2 a}\)
2. \(d < \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)
3. \(d > \frac{\left(v_{1} - v_{2}\right)^{2}}{2 a}\)
4. \(d > \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)
| 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. |
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 \(x^2= t^2+1\)
1. \(\frac{1}{x}\)
2. \(\frac{1}{x} - \frac{1}{x^{3}}\)
3. \(\frac{2}{x}\)
4. \(-\frac{t^2}{x^3}\)
The position \(x\) of a particle moving along the \(x\)-axis varies with time \(t\) as \(x=20t-5t^2,\) where \(x\) is in meters and \(t\) is in seconds. The particle reverses its direction of motion at:
1. \(x=40~\text{m}\)
2. \(x=10~\text{m}\)
3. \(x=20~\text{m}\)
4. \(x=30~\text{m}\)
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