A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to where and \(\mathrm{n}\) are constants and \(\mathrm{x}\) is the position of the particle. The acceleration of the particle as a function of \(\mathrm{x}\) is given by:
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2.
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4.
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-2 |
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 \(\mathrm{X}\) to \(\mathrm{Y}\) with a uniform speed \(\mathrm{v_u}\) and returns to \(\mathrm{X}\) with a uniform speed \(\mathrm{v_d}.\) The average speed for this round trip is:
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A particle moves along a straight line OX. At a time t (in seconds), the displacement x (in metres) of the particle from O is given by x= 40 + 12t – t3. How long would the particle travel before coming to rest?
1. | 24 m | 2. | 40 m |
3. | 56 m | 4. | 16 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 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. |
A car A is traveling on a straight level road at a uniform speed of 60 km/h. It is followed by another car B which is moving at a speed of 70 km/h. When the distance between them is 2.5 km, car B is given a deceleration of 20 km/h2. After how much time will car B catch up with car A?
1. 1 hr
2. 1/2 hr
3. 1/4 hr
4. 1/8 hr
The graph of displacement time is given below.
Its corresponding velocity-time graph will be:
1. | 2. | ||
3. | 4. |
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. | \(\frac{3A}{2}+4B\) |