A particle is moving with a velocity of $\mathrm{v}=(3+6\mathrm{t}) {\mathrm{cms}}^{-1}$. The displacement of the particle in the interval t=0 sec to t=5 sec is:

1. 75 cm

2. 20 cm

3. 50 cm

4. 90 cm

A body moved in a straight line according to equation $\mathrm{x}=30\mathrm{t}-5{\mathrm{t}}^2$. Th value of $\frac{\left|\mathrm{displacement}\right|}{\mathrm{distance}}$ between t=2 s to t=5 s is

1. >1

2. =1

3. <1

4. =2

A body has an initial velocity of 3 m/s and has an acceleration of 1 m/s² normal to the direction of the initial velocity. Then its velocity 4 seconds after the start is:

(1) 7 m/s along the direction of initial velocity

(2) 7 m/s along the normal to the direction of initial velocity

(3) 7 m/s mid-way between the two directions

(4) 5 m/s at an angle of tan^–1 (4/3) with the direction of initial velocity

A graph between square of speed with time t for a particle moving on a straight line. The acceleration of the particle at t=1 s is

1. $1 \mathrm{m}/{\mathrm{s}}^2$

2. $1.5 \mathrm{m}/{\mathrm{s}}^2$

3. $2.0 \mathrm{m}/{\mathrm{s}}^2$

4. $2.5 \mathrm{m}/{\mathrm{s}}^2$

The acceleration (a) versus time (t) graph of a particle moving along a straight line is shown in the given figure. The particle starts from rest at t=0. The velocity of the particle is maximum at
             

1. t=2 s
2. t=4 s
3. t=6 s
4. t=3 s

The acceleration-time graph of a particle moving along a straight line is given. At what time, the speed of a particle becomes equal to its initial speed?

      
1. 10 s
2. 8 s
3. 6 s
4. 4 s

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

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

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

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. $-2 m/s^2$