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. \(0\) m
4. none of the above
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. \(x=30~\text{m}\)
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 \((x\text-t)\) 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 \(-{v_0T} \lt x \lt {v_0T}\). |
3. | the acceleration is always a non-negative number. |
4. | the motion has no turning points. |