A car is moving along east at \(10\) m/s and a bus is moving along north at \(10\) m/s. The velocity of the car with respect to the bus is along:

1.	North-East	2.	South-East
3.	North-West	4.	South-West

A particle is moving on a circular path of radius 1m with a constant speed of 1 m/s. Acceleration of the particle is:

1.  $\sqrt{2}\mathrm{m}/{\mathrm{s}}^2$

2.  $\frac{1}{\sqrt{2}}\mathrm{m}/{\mathrm{s}}^2$

3.  $1 \mathrm{m}/{\mathrm{s}}^2$

4.  0

A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{{v}}=4 \hat{{i}}+2 {t} \hat{{j}}\). The trajectory of the particle is correctly shown in the figure:

1.		2.
3.		4.

A particle is moving in the \(XY\) plane such that \(x = \left(t^2 -2t\right)~\text m,\) and \(y = \left(2t^2-t\right)~\text m,\) then:

Rain is pouring vertically downward at a velocity of \(4~\text{km/h}\). The magnitude of the velocity of rain with respect to a man running along the north on a horizontal road at \(3~\text{km/h}\) is:
1. \(7~\text{km/h}\)
2. \(5~\text{km/h}\)
3. \(1~\text{km/h}\)
4. \(3~\text{km/h}\)

A particle is moving with an acceleration of $\overrightarrow{\mathrm{a}} = 3{\mathrm{t}}^2\hat{\mathrm{i}} + 2\mathrm{t}\hat{\mathrm{j}} \mathrm{m}/{\mathrm{s}}^2$. If at t = 0, its velocity is (i+j) m/s, then its velocity (in m/s) at time t = 2 s is

(1) $9\hat{\mathrm{i}} + 5\hat{\mathrm{j}}$

(2) $8\hat{\mathrm{i}} + 4\hat{\mathrm{j}}$

(3) $5\hat{\mathrm{i}} - 9\hat{\mathrm{j}}$

(4) $6\hat{\mathrm{i}} - 8\hat{\mathrm{j}}$

It is raining at \(20\) m/s in still air. Now a wind starts blowing with speed \(10\) m/s in the north direction. If a cyclist starts moving at \(10\) m/s in the south direction, then the apparent velocity of rain with respect to a cyclist will be:
1. \(20\) m/s
2. \(20\sqrt{2}\) m/s
3. \(10 \sqrt{5}\) m/s
4. \(30\) m/s

Path of a projectile with respect to another projectile so long as both remain in the air is:
1. Circular
2. Parabolic
3. Straight
4. Hyperbolic

A missile is fired for maximum range with an initial velocity of \(20\) m/s, then the maximum height of missile is: (Take \(g=10\) m/s²)
1. \(20\) m
2. \(30\) m
3. \(10\) m
4. \(40\) m

A particle is moving along a circle of radius \(R \) with constant speed \(v_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?