A body starts moving from rest on a horizontal ground such that the position vector of the body with respect to its starting point is given by $\mathrm{r}$ $=$ $2\mathrm{t}\hat{\mathrm{i}}$ $+$ $3{\mathrm{t}}^2\hat{\mathrm{j}}$. The equation of the trajectory of the body is:

1. y = 1.5 x

2. y = 0.75 ${\mathrm{x}}^2$

3. y = 1.5 ${\mathrm{x}}^2$

4. y = 0.45 ${\mathrm{x}}^2$

A particle starts moving with constant acceleration with initial velocity (\(\hat{\mathrm{i}}+5\hat{\mathrm{j}}\)$\stackrel{}{\mathrm{}}$) m/s. After \(4\) seconds, its velocity becomes (\(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}\)) m/s. The magnitude of its displacement in 4 seconds is:
1. \(5\) m
2. \(10\) m
3. \(15\) m
4. \(20\) m

A particle is revolving in a circular path of radius 200 m at a speed of 20 m/s. Its speed is increasing at a rate of $\sqrt{5}$ $\mathrm{m}/{\mathrm{s}}^2$. Its acceleration is :

(1) 2 $\mathrm{m}/{\mathrm{s}}^2$

(2) $\sqrt{7}$ $\mathrm{m}/{\mathrm{s}}^2$

(3) 3 $\mathrm{m}/{\mathrm{s}}^2$

(4) $\sqrt{5}$ $\mathrm{m}/{\mathrm{s}}^2$

The ratio of maximum height attained by two projectiles of the same mass is 25: 9. The ratio of their minimum kinetic energy is 4: 9. The ratio of their ranges is:

(1) 25: 4

(2) 10: 9

(3) 5: 2

(4) 1: 1

If a particle is moving in a circular orbit with constant speed, then:

In a uniform circular motion,

(1) Both velocity and acceleration are constant.

(2) Acceleration and speed are constant but velocity changes.

(3) Both acceleration and velocity change.

(4) Both acceleration and speed are constant.

The relative velocity of a car P with respect to Q is $20\sqrt{2}$ m/s North-East. The velocity of car Q is 40 m/s due to South. The velocity of car P is:

(1) 20 m/s East

(2) $20\sqrt{2}$ m/s South-East

(3) 20 m/s West

(4) $20\sqrt{2}$ m/s North-West

A projectile is projected with initial kinetic energy K. If it has kinetic energy 0.25K at its highest point, then the angle of projection is:

1. 30°

2. 45°

3. 60°

4. 75°

A body is projected from the ground at an angle of 30° with horizontal. The instantaneous velocity of the body becomes perpendicular to initial velocity during its motion:

(1) Once

(2) Twice

(3) Thrice

(4) Never

In the uniform circular motion, which of the following physical quantity remains constant?

(1) Angular velocity

(2) Angular momentum

(3) Angular speed

(4) All of these