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$s^{-2}$)

(1) $1500\sqrt{2} m{s}^{-2} upwards$

(2) $1800 m{s}^{-2} downwards$

(3) $1500\sqrt{5} m{s}^{-2} upwards$

(4) $1500\sqrt{2} m{s}^{-2} downwards$

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?
\((g = 10~\text{m/s}^2)\)

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) $\sqrt{a^2+g^2} and g$

(4) $\sqrt{a^2+g^2} and a$

The x and y coordinates of the particle at any time are $\mathrm{x}=5\mathrm{t}-2{\mathrm{t}}^2$ 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 $\mathrm{m}/{\mathrm{s}}^2$

3. -4 $\mathrm{m}/{\mathrm{s}}^2$

4. -8 $\mathrm{m}/{\mathrm{s}}^2$

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 engine of a motorcycle can produce a maximum acceleration 5 m/s². Its brakes can produce a maximum retardation 10 m/s². What is the minimum time in which it can cover a distance of 1.5 km?

(1) 30 sec

(2) 15 sec

(3) 10 sec

(4) 5 sec

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (Given $g=9.8m/s^2)$

(1) At least 0.8 m/s

(2) Any speed less than 19.6 m/s

(3) Only with speed 19.6 m/s

(4) More than 19.6 m/s

Read the assertion and reason carefully to mark the correct option out of the options given below:

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false.

Assertion : The equation of motion can be applied only if acceleration is along the direction of velocity and is constant.

Reason : If the acceleration of a body is constant then its motion is known as uniform motion.

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 point moves in a straight line so that its displacement x metre at time t sec is given by ${\mathrm{x}}^2=1+{\mathrm{t}}^2$ . Its acceleration in m/s² at time t sec is

1. $\frac{1}{{\mathrm{x}}^3}$

2. $\frac{1}{\mathrm{x}}-\frac{1}{x^2}$

3. $\frac{1}{\mathrm{x}}-\frac{t^2}{x^3}$

4. $\frac{-\mathrm{t}}{{\mathrm{x}}^2}$