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.
\(\frac{3A}{2}+4B\)
1. \(- 2 nβ^{2} x^{- 2 n - 1}\)
2. \(- 2 nβ^{2} x^{- 4 n - 1}\)
3. \(- 2 \beta^{2} x^{- 2 n + 1}\)
4. \(- 2 nβ^{2} x^{- 4 n + 1}\)
A stone falls freely under gravity. It covers distances \(h_1,~h_2\) and \(h_3\) in the first \(5\) seconds, the next \(5\) seconds and the next \(5\) seconds respectively. The relation between \(h_1,~h_2\) and \(h_3\) is:
| 1. | \(h_1=\frac{h_2}{3}=\frac{h_3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \) |
| 2. | \(h_2=3h_1\) and \(h_3=3h_2\) |
| 3. | \(h_1=h_2=h_3\) |
| 4. | \(h_1=2h_2=3h_3\) |
A ball is dropped from a high-rise platform at \(t=0\) starting from rest. After \(6\) seconds, another ball is thrown downwards from the same platform with speed \(v\). The two balls meet after \(18\) seconds. What is the value of \(v\)?
| 1. | \(75\) ms-1 | 2. | \(55\) ms-1 |
| 3. | \(40\) ms-1 | 4. | \(60\) ms-1 |
A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\) ms-1 to \(20\) ms-1 while covering a distance of \(135\) m in \(t\) seconds. The value of \(t\) is:
| 1. | \(10\) | 2. | \(1.8\) |
| 3. | \(12\) | 4. | \(9\) |
A car moves from \(X\) to \(Y\) with a uniform speed \(v_u\) and returns to \(X\) with a uniform speed \(v_d.\) The average speed for this round trip is:
| 1. | \(\dfrac{2 v_{d} v_{u}}{v_{d} + v_{u}}\) | 2. | \(\sqrt{v_{u} v_{d}}\) |
| 3. | \(\dfrac{v_{d} v_{u}}{v_{d} + v_{u}}\) | 4. | \(\dfrac{v_{u} + v_{d}}{2}\) |
| 1. | \(24~\text m\) | 2. | \(40~\text m\) |
| 3. | \(56~\text m\) | 4. | \(16~\text m\) |
A ball is dropped vertically from a height \(h\) above the ground. It hits the ground and bounces up vertically to a height of \(\frac{h}{2}\). Neglecting subsequent motion and air resistance, its velocity \(v\) varies with the height \(h\) as:
[Take vertically upwards direction as positive.]
| 1. |  |
2. |  |
| 3. |  |
4. |  |
The graph of displacement time is given below.
Its corresponding velocity-time graph will be:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A particle moves along a straight line and its position as a function of time is given by \(x= t^3-3t^2+3t+3\)
| 1. | stops at \(t=1~\text{s}\) and reverses its direction of motion. |
| 2. | stops at \(t= 1~\text{s}\) and continues further without a change of direction. |
| 3. | stops at \(t=2~\text{s}\) and reverses its direction of motion. |
| 4. | stops at \(t=2~\text{s}\) and continues further without a change of direction. |
© 2025 GoodEd Technologies Pvt. Ltd.