For a projectile, the angle between the velocity and the x-axis as a function of time is given by:

$\left(1\right)<mspace\; width="1em"></mspace>\mathrm{\theta }\left(\mathrm{t}\right)={\cos }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}-\mathrm{gt}}{{\mathrm{u}}_{\mathrm{x}}}\right)$

$\left(2\right)<mspace\; width="1em"></mspace>\mathrm{\theta }\left(\mathrm{t}\right)={\sin }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}-\mathrm{gt}}{{\mathrm{u}}_{\mathrm{x}}}\right)$

$\left(3\right)<mspace\; width="1em"></mspace>\mathrm{\theta }\left(\mathrm{t}\right)={\cot }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}-\mathrm{gt}}{{\mathrm{u}}_{\mathrm{x}}}\right)$

$\left(4\right)<mspace\; width="1em"></mspace>\mathrm{\theta }\left(\mathrm{t}\right)={\tan }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}-\mathrm{gt}}{{\mathrm{u}}_{\mathrm{x}}}\right)$

A truck starts from rest and accelerates uniformly at \(2.0~\text{ms}^{-2}\). At \(t = 10~\text{s}\), a stone is dropped by a person standing on the top of the truck (\(6\) m high from the ground). What is the acceleration of the stone at \(t = 11~\text{s}\)? (Neglect air resistance.)
1. \(10\) ms^–2 (upward)
2. \(15\) ms^–2 (downward)
3. \(10\) ms^–2 (downward)
4. \(15\) ms^–2 (upward)

A particle is moving along a circle such that it completes one revolution in \(40\) seconds. In \(2\) minutes \(20\) seconds, the ratio of \(|displacement| \over distance\) will be:
1. \(0\)
2. \(\dfrac{1}{7}\)
3. \(\dfrac{2}{7}\)
4. \(\dfrac{1}{11}\)

Consider the motion of the tip of the second hand of a clock. In one minute (assuming \(R\) to be the length of the second hand), its:

A car moves with a speed of \(60\) km/h for \(1\) hour in the east direction and with the same speed for \(30\) min in the south direction. The displacement of the car from the initial position is:

At any instant, the velocity and acceleration of a particle moving along a straight line are v and a. The speed of the particle is increasing if

(1) v>0, a>0

(2) v<0, a>0

(3) v>0, a<0

(4) v>0, a=0

If v is the velocity of a body moving along x-axis, then acceleration of body is

(1) $\frac{dv}{dx}$

(2) $v\frac{dv}{dx}$

(3) $x\frac{du}{dx}$

(4) $v\frac{dx}{dv}$

If a body is moving with constant speed, then its acceleration

1. Must be zero

2. May be variable

3. May be uniform

4. Both (2) & (3)

An object is moving with variable speed, then

(1) Its velocity may be zero

(2) Its velocity must be variable

(3) Its acceleration may be zero

(4) Its velocity must be constant

If the displacement of a particle varies with time as $\sqrt{x}=t+7$, then

(1) Velocity of the particle is inversely proportional to t

(2) Velocity of the particle is proportional to t²

(3) Velocity of the particle is proportional to $\sqrt{t}$

(4) The particle moves with constant acceleration.