A police jeep is chasing with velocity of 45 km/h. A thief in another jeep moving with velocity 153 km/h. Police fires a bullet with muzzle velocity of 180 m/s. The velocity it will strike the car of the thief is

• 150 m/s

• 27 m/s

• 450 m/s

• 250 m/s

Two similar charges having mass m and 2m are placed in an electric field. The ratio of their kinetic energy is :

• 4:1

• 1:1

• 2:1

• 1:2

A car starts from rest, moves with an acceleration a and then decelerates at a constant rate b for sometimes to come to rest. If the total time taken is t. The maximum velocity of car is given by :

• $\frac{\mathrm{a} \mathrm{b} \mathrm{t}}{\left(\mathrm{a} + \mathrm{b} \right)}$

• $\frac{{\mathrm{a}}^2 \mathrm{t}}{\mathrm{a} + \mathrm{b}}$

• $\frac{\mathrm{a} \mathrm{t}}{\left(\mathrm{a}+ \mathrm{b}\right)}$

• $\frac{{\mathrm{b}}^2 \mathrm{t}}{\mathrm{a}+\mathrm{b}}$

A river is flowing from west to east with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so, as to take the shortest possible path to go to the south?

• 30^o east of south

• 60^o east of south

• 60^o west of south

• 30^o west of north

Two boys are standing at the ends A and B of a ground, where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v₁ The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is 

• $\frac{\mathrm{a}}{\sqrt{{\mathrm{v}}^2 + {\mathrm{v}}_1^2}}$

• $\sqrt{\frac{{\mathrm{a}}^2}{{\mathrm{\nu }}^2 - {\mathrm{\nu }}_1^2}}$

• $\frac{\mathrm{a}}{\left(\mathrm{\nu } - {\mathrm{\nu }}_1\right)}$

• $\frac{\mathrm{a}}{\left(\mathrm{\nu } + {\mathrm{\nu }}_1\right)}$

A ball is thrown vertically upward. It has a speed of 10 m/s when it has reached one-half of its maximum height. How high does the ball rise? ( Take, g = 10 m/s² )

• 15 m

• 10 m

• 20 m

• 5 m

A car moves from X to Y with a uniform speed v_u and returns to Y with a uniform speed v_d The average speed for this round trip is

• $\frac{2 {\mathrm{\nu }}_{\mathrm{d} }{\mathrm{\nu }}_{\mathrm{u}}}{{\mathrm{\nu }}_{\mathrm{d}} + {\mathrm{\nu }}_{\mathrm{u}}}$

• $\sqrt{{\mathrm{v}}_{\mathrm{u} }{\mathrm{v}}_{\mathrm{d}}}$

• $\frac{{\mathrm{v}}_{\mathrm{d} }{\mathrm{v}}_{\mathrm{u}}}{{\mathrm{v}}_{\mathrm{d}} + {\mathrm{v}}_{\mathrm{u}}}$

• $\frac{{\mathrm{v}}_{\mathrm{u}} + {\mathrm{v}}_{\mathrm{d}}}{2}$

A particle moves along a straight line OX. At a time t (in second) the distance x ( in metre ) of the particle from O is given by x = 40 + 12 t - t³ . How long would the particle travel before coming to rest?

• 24 m

• 40 m

• 56 m

• 16 m

A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc?

• 0.4 cm

• 2.4 cm

• 1.8 cm

• 1.2 cm

The displacement of particle is given by $\mathrm{x} = {\mathrm{\alpha }}_{\mathrm{o}}+ \frac{{\mathrm{\alpha }}_1\mathrm{t}}{2} - \frac{{\mathrm{\alpha }}_2{\mathrm{t}}^2}{3}$ .What is its acceleration?

• $\frac{2{\mathrm{\alpha }}_2}{3}$

• $-\frac{2{\mathrm{\alpha }}_2}{3}$

• ${\mathrm{\alpha }}_2$

• Zero