A car moves on a circular path such that its speed is given by \(v= Kt\), where \(K\) = constant and \(t\) is time. Also given: radius of the circular path is \(r\). The net acceleration of the car at time \(t\) will be:
1. \(\sqrt{K^{2} +\left(\frac{K^{2} t^{2}}{r}\right)^{2}}\)
2. \(2K\)
3. \(K\)
4. \(\sqrt{K^{2}   +   K^{2} t^{2}}\)

An object of mass 10 kg is projected from level ground with speed 40 m/s at angle 30° with horizontal. The rate of change of momentum of object [in SI units] 1 second after the projection is [neglect air resistance]

(1) 100

(2) 50

(3) 25

(4) 75

A particle is projected horizontally with speed 20 m/s from a cliff of height 20 m. The magnitude of the velocity of particle when it reaches the ground

1. 20 m/s

2. 40 m/s

3. 20$\sqrt{2}$ m/s

4. Zero

A projectile is thrown with an initial velocity of 20 m/s at an angle of 60° with horizontal, then the angle of the velocity of the projectile with horizontal after time 0.732 sec is:

(1) 45°

(2) 30°

(3) 0°

(4) 15°

If ${\mathrm{a}}_{\mathrm{r}} \mathrm{and} {\mathrm{a}}_{\mathrm{t}}$ represent radial and tangential accelerations, then the motion of particle will be uniformly circular for :

(1) ${\mathrm{a}}_{\mathrm{r}}$ = 0, ${\mathrm{a}}_{\mathrm{t}}$ = 0

(2) ${\mathrm{a}}_{\mathrm{r}}$ = 0, ${\mathrm{a}}_{\mathrm{t}}$ $\ne$ 0

(3) ${\mathrm{a}}_{\mathrm{r}}$ $\ne$ 0, ${\mathrm{a}}_{\mathrm{t}}$ = 0

(4) ${\mathrm{a}}_{\mathrm{r}}$ $\ne$ 0, ${\mathrm{a}}_{\mathrm{t}}$ $\ne$ 0

A helicopter flies from a city A to B. The line joining A and B is along North-South direction and its length is 100 km. The speed of the helicopter is kept 100 km/h and the wind blows from West to East with a speed of 60 km/h. The time taken by the helicopter is

(1) 0.75 h

(2) 1.0 h

(3) 1.25 h

(4) 1.33 h

Four particles lie initially at the corners of a square of side length L. All the particles start to move with speed v. A moves towards B, B moves towards C, C moves towards D and D moves towards A. The distance covered by a particle till they meet is

(1) $\frac{\mathrm{L}}{\sqrt{5}}$

(2) L

(3) $\sqrt{2}\mathrm{L}$

(4) 2L

A boat can move with a maximum speed of 10 m/s in still water. If the speed of river water is 5 m/s, then in how much minimum time the boat can cross the river of width 500 m?

(1) $\frac{100}{\sqrt{5}}$ s

(2) 50 s

(3) 100 s

(4) 150 s

A particle is thrown at an angle of projection $\mathrm{\theta }$ = 45° with speed u. The average velocity of the particle during its ground to ground flight is

1.  $\sqrt{2}\mathrm{u}$

2.  $\frac{\mathrm{u}}{\sqrt{2}}$

3.  $\frac{\mathrm{u}}{2}$

4.  0

The raindrops are falling with speed \(v\) vertically downwards and a man is running on a horizontal road with speed \(u.\) The magnitude of the velocity of the raindrops with respect to the man is:
1. \(v-u\)
2. \(v+u\)
3. \(\sqrt{{v}^2 + {u}^2 \over 2}\)
4. \(\sqrt{{v}^2 + {u}^2}\)