A particle starts its motion from rest under the action of a constant force. If the distance covered in the first \(10\) s is \(S_1\) and that covered in the first \(20\) s is \(S_2\), then:
1. \(S_2=2S_1\)
2. \(S_2 = 3S_1\)
3. \(S_2 = 4S_1\)
4. \(S_2= S_1\)
The distance travelled by a particle starting from rest and moving with an acceleration \(\frac{4}{3}\) ms-2, in the third second is:
1. \(6\) m
2. \(4\) m
3. \(\frac{10}{3}\) m
4. \(\frac{19}{3}\) m
A particle shows the 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 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. | \(9\) |
The position of a particle with respect to time \(t\) along the \(\mathrm{x}\)-axis is given by \(x=9t^{2}-t^{3}\) where \(x\) is in metres and \(t\) in seconds. What will be the position of this particle when it achieves maximum speed along the \(+\mathrm{x} \text-\text{direction}?\)
1. \(32\) m
2. \(54\) m
3. \(81\) m
4. \(24\) m
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. | \(\dfrac{v_{u} + v_{d}}{2}\) |
A particle moving along the x-axis has acceleration \(f,\) at time \(t,\) given by, \(f=f_0\left ( 1-\frac{t}{T} \right ),\) where \(f_0\) and \(T\) are constants. The particle at \(t=0\) has zero velocity. In the time interval between \(t=0\) and the instant when \(f=0,\) the particle’s velocity \( \left ( v_x \right )\) is:
1. \(f_0T\)
2. \(\frac{1}{2}f_0T^{2}\)
3. \(f_0T^2\)
4. \(\frac{1}{2}f_0T\)
1. | \(24~\text m\) | 2. | \(40~\text m\) |
3. | \(56~\text m\) | 4. | \(16~\text m\) |
Two bodies, \(A\) (of mass \(1~\text{kg}\)) and \(B\) (of mass \(3~\text{kg}\)) are dropped from heights of \(16~\text{m}\) and \(25~\text{m}\), respectively. The ratio of the time taken by them to reach the ground is:
1. \(\frac{5}{4}\)
2. \(\frac{12}{5}\)
3. \(\frac{5}{12}\)
4. \(\frac{4}{5}\)