A man is at a distance of  6 m from a bus. The bus begins to move with a constant acceleration of 3ms.In order to catch the bus, the minimum speed with which the man should run towards the bus is

• 2 m s^-1

• 4 m s^-1

• 6 m s^-1

• 8 m s^-1

A ball is dropped from the top of a building 100 m high. At the same instant another ball is thrown upwards with a velocity of 40 m/s from the bottom of the building. The two balls will meet after

• 3 s

• 2 s

• 2.5 s

• 5 s

The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is proportional to

• $\sqrt{\mathrm{t}}$

• t

• t²

• t^3/2

Assertion: The speedometer of an automobile measures the average speed of the automobile. 

Reason:  Average velocity is equal to total distance divided by total time taken.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false.

• If both assertion and reason are false.

145.

A particle is moving eastwards with a velocity of 5 m/s. In 10 s, the velocity changes to 5 m/s northwards. The average acceleration in this time is

• zero

• 1/√2 m s^-2 towards north-west

• 1/√2 m s^-2 towards north-east

• 1/√2 m s^-2 towards north

Assertion:  The relative velocity between any two bodies moving in opposite direction is equal to sum of the velocities of two bodies. 

Reason:  Sometimes relative velocity between two bodies is equal to difference in velocities of the two bodies.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

If a vector $2 \hat{\mathrm{i}} + 3 \hat{\mathrm{j}} + 8 \hat{\mathrm{k}}$ is perpendicular to the vector $4 \hat{\mathrm{i}} - 4 \hat{\mathrm{j}} + \mathrm{\alpha } \hat{\mathrm{k}}$, then value of α is

• -1

• $\frac{1}{2}$

• $- \frac{1}{2}$

• 1

A particle is thrown vertically upwards with velocity 11.2 km s1 from the surface of earth. Calculate its velocity at height 3 R. Where R is the radius of earth

• $\simeq$ 9.25 km s^-1

• $\simeq$ 5.6 km s^-1

• $\simeq$ 11.2 km s^-1

• $\simeq$ 4.3 km s^-1

Water is flowing with velocity 4 m s^-1 in a cylinder of diameter 8 cm, it is connected to a pipe with it end tip of diameter 2 cm, calculate the velocity of water at this free end.

• 4 m s^-1

• 8 m s^-1

• 32 m s^-1

• 64 m s^-1

If maximum speed in SHM is given by V_m, what is its average speed?

• $\frac{\mathrm{\pi }}{2}$ V_m

• $\frac{2}{\mathrm{\pi }}$ V_m

• $\frac{\mathrm{\pi }}{4}$ V_m

• $\frac{{\mathrm{V}}_{\mathrm{m}}}{\sqrt{2}}$