Two particles \(\mathrm{A}\) and \(\mathrm{B}\), move with constant velocities \(\overrightarrow{{v}_1}\) and \(\overrightarrow{{v}_2}\) respectively. At the initial moment, their position vectors are \(\overrightarrow{{r}_1}\) and \(\overrightarrow{{r}_2}\) respectively. The condition for particles \(\mathrm{A}\) and \(\mathrm{B}\) for their collision will be:
1. \(\vec{r_1} \cdot \vec{v_1}=\vec{r_2} \cdot \vec{v_2}\)
2. \(\dfrac{\vec{r_1}-\vec{r_2}}{\left|\vec{r_1}-\vec{r_2}\right|}=\dfrac{\vec{v_2}-\vec{v_1}}{\left|\vec{v_2}-\vec{v_1}\right|}\)
3. \(\vec{r_1} \times \vec{v_1}=\vec{r_2} \times \vec{v_2}\)
4. \(\vec{r_1}-\vec{r_2}=\vec{v_1}-\vec{v_2}\)
A point moves in a straight line so that its displacement x metre at time t sec is given by . Its acceleration in m/s2 at time t sec is
1.
2.
3.
4.
A ball is falling freely strikes to ground with velocity
60 m/s. Height fallen in last one second before
hitting the ground is
1. 55 m
2. 70 m
3. 60 m
4. 80 m
The x and y coordinates of the particle at any time are and y = 10 t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is
1. 0
2. 5
3. -4
4. -8
A bus moves over a straight level road with a constant acceleration a. A body in the bus drops a ball outside. The acceleration of the ball with respect to the bus and the earth are respectively
(1) a and g
(2) a + g and g - a
(3)
(4)
A ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 s, the average acceleration during contact is nearly (Take g = 10 m)
(1)
(2)
(3)
(4)
Two bullets are fired horizontally and simultaneously towards each other from the rooftops of two buildings (building being \(100~\text{m}\) apart and being of the same height of \(200~\text{m}\)) with the same velocity of \(25~\text{m/s}.\) When and where will the two bullets collide?
\((g = 10~\text{m/s}^2)\)
1. | After \(2~\text{s}\) at a height of \(180~\text{m}\) |
2. | After \(2~\text{s}\) at a height of \(20~\text{m}\) |
3. | After \(4~\text{s}\) at a height of \(120~\text{m}\) |
4. | They will not collide. |
A point moves in a straight line under the retardation . If the initial velocity is u, the distance covered in 't' second is-
1. aut
2.
3.
4.
The relation between time and distance is , where and are constants. The retardation is
1.
2.
3.
4.
A particle moves along a parabolic path \(y =9x^2\) in such a way that the \(x\) component of the velocity remains constant and has a value of \(\frac{1}{3}~\text{m/s}\). It can be deduced that the acceleration of the particle will be:
1. \(\frac{1}{3}\hat j~\text{m/s}^2\)
2. \(3\hat j~\text{m/s}^2\)
3. \(\frac{2}{3}\hat j~\text{m/s}^2\)
4. \(2\hat j~\text{m/s}^2\)