The velocity of a particle moving along a straight line with constant acceleration 'a' reduces to $\frac{1}{5}$ of its initial velocity in time $\text{'}\tau \text{'}$. The total time taken by the body till its velocity becomes zero is:

1. $\frac{4\tau }{3}$

2. $\frac{5\tau }{4}$

3. $\frac{4\tau }{5}$

4. $\frac{3\tau }{4}$

A boy falls from a building of height 320 m. After 5 seconds, superman jumps downward with initial speed u such that the boy can be saved. The minimum value of u is (assume g=10 $\mathrm{m}/{\mathrm{s}}^2$)

The displacement x of a body having relation with time as $\mathrm{x}=3{\mathrm{t}}^2-6\mathrm{t}+7$, then distance covered by body in first two second is [where x is in metre and t is in second].

1. Zero

2. 6 m

3. 3 m

4. 9 m

The acceleration of particle for which the ${\mathrm{v}}^2$ versus s graph is shown is:
                 
1. - 8 $\mathrm{m}/{\mathrm{s}}^2$
2. 4 $\mathrm{m}/{\mathrm{s}}^2$
3. - 4 $\mathrm{m}/{\mathrm{s}}^2$
4. -16 $\mathrm{m}/{\mathrm{s}}^2$

Assertion: A body is momentarily at rest when it reverses the direction of motion.
Reason: A body cannot have acceleration if its velocity is zero at a given instant of time.

1. both Assertion and Reason are true and the reason is the correct explanation of the assertion.
2. both Assertion and Reason are true but the reason is not the correct explanation of the assertion.
3. Assertion is a true statement but Reason is false.
4. both Assertion and Reason are false statements.

The position (x) of a particle moving along x-axis varies with time (t) as $\mathrm{x}={\mathrm{t}}^2-4\mathrm{t}+5$. The particle turns around at

1. t=1 s

2. t=2 s

3. t=3 s

4. t=4 s

The velocity (v) of a particle varies with position (x) as shown in the graph. Its acceleration when x=4 m will be

1. $-8 \mathrm{m}/{\mathrm{s}}^2$

2. $8 \mathrm{m}/{\mathrm{s}}^2$

3. $2 \mathrm{m}/{\mathrm{s}}^2$

4. $-2 m/s^2$

The acceleration time graph of a particle moving along a straight line is shown in the figure. The time taken by the particle to acquire its initial velocity is?

1. 4 s
2. 8 s
3. 10 s
4. 5 s

Position of a particle moving on a straight line is given by $\mathrm{x}=2{\mathrm{t}}^2-6\mathrm{t}$. The distance travelled by the particle in first four seconds is

1. 3 m

2. 17 m

3. 22 m

4. 28 m

A bird flies for 4 s with a velocity of |t-2| m/s in a straight line, where t is time in seconds. It covers a distance of

1. 2 m

2. 4 m

3. 6 m

4. 8 m