Q. No.If the velocity of a particle is \(v=At+Bt^{2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1~\text{s}\) and \(2~\text{s}\) is:
| 1. | \(3A+7B\) | 2. | \(\frac{3}{2}A+\frac{7}{3}B\) |
| 3. | \(\frac{A}{2}+\frac{B}{3}\) | 4. | \(\frac{3A}{2}+4B\) |
The displacement \((x)\) of a point moving in a straight line is given by; \(x=8t^2-4t.\) Then the velocity of the particle is zero at:
| 1. | \(0.4\) s | 2. | \(0.25\) s |
| 3. | \(0.5\) s | 4. | \(0.3\) s |
The position of an object moving along the x-axis is given by, \(x=a+bt^2\) where \(a=8.5\) m, \(b=2.5\) ms-2, and \(t\) is measured in seconds. Its velocity at \(t=2.0\) s will be:
1. \(13\) m/s
2. \(17\) m/s
3. \(10\) m/s
4. \(0\)
For a particle, displacement time relation is given by . Its displacement, when its velocity is zero will be:
1. \(2\) m
2. \(4\) m
3. \(0\)
4. none of the above
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
1. \(12\) ms-1
2. \(20\) ms-1
3. \(36\) ms-1
4. \(46\) ms-1
A body in one-dimensional motion has zero speed at an instant. At that instant, it must have:
| 1. | zero velocity. | 2. | zero acceleration. |
| 3. | non-zero velocity. | 4. | non-zero acceleration. |
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 position-time \((x-t)\) graphs for two children \(A\) and \(B\) returning from their school O to their homes P and Q respectively are shown in the graph. Choose the incorrect statement.
| 1. | \(B\) reaches home faster than \(A.\) |
| 2. | \(B\) overtakes \(A\) on the road twice. |
| 3. | \(B\) walks faster than \(A.\) |
| 4. | \(A\) lives closer to the school than \(B.\) |
If in one-dimensional motion, instantaneous speed \(v\) satisfies \(0\leq v<v_0\), then:
| 1. | the displacement in time \(T\) must always take non-negative values. |
| 2. | the displacement \(x\) in time \(T\) satisfies \(-\mathrm{v_0T} \lt x \lt \mathrm{v_0T}\). |
| 3. | the acceleration is always a non-negative number. |
| 4. | the motion has no turning points. |
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