A particle is moving with constant acceleration from A to B in a straight line AB. If u and v are the velocities at A and B respectively then its velocity at the midpoint C will be

• $\left(\frac{{\mathrm{u}}^2 + {\mathrm{v}}^2}{2\mathrm{u}}\right)$

• $\frac{\mathrm{u} + \mathrm{v}}{2}$

• $\frac{\mathrm{v} - \mathrm{u}}{2}$

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

An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10 s apart is 30°, then the speed of the aircraft is

• 19.63 ms^-1

• 1963 ms^-1

• 108 ms^-1

• 196.3 ms^-1

33.

A particle crossing the origin of co-ordinates at time t = 0, moves in the xy-plane with a constant acceleration a in the y-direction. If its equation of motion is y = bx² (b is a constant), its velocity component in the x-direction is

• $\sqrt{\frac{2\mathrm{b}}{\mathrm{a}}}$

• $\sqrt{\frac{\mathrm{a}}{2\mathrm{b}}}$

• $\sqrt{\frac{\mathrm{a}}{\mathrm{b}}}$

• $\sqrt{\frac{\mathrm{b}}{\mathrm{a}}}$

A stationary bomb explodes into three pieces. One piece of 2 kg mass moves with a velocity of 8 ms^-1 at right angles to the other piece of mass 1 kg moving with a velocity of 12 ms^-1. If the mass of the third piece of 0.5 kg, then its velocity is 

• 10 ms^-1

• 20 ms^-1

• 30 ms^-1

• 40 ms^-1

A bridge is in the form of a semi-circle of radius 40 m. The greatest speed with which a motor cycle can cross the bridge without leaving the ground at the highest point is (g =10 ms^-2) (Frictional force is negligibly small)

• 40 ms^-1

• 20 ms^-1

• 30 ms^-1

• 15 ms^-1

A body travelling with uniform acceleration crosses two points A and B with velocities 20 ms^-1 and 30 ms^-1 respectively. The speed of the body at the mid-point of A and B is nearest to

• 25.5 ms^-1

• 25 ms^-1

• 24 ms^-1

• $10\sqrt{6} {\mathrm{ms}}^{-1}$

An aeroplane flies around a square field ABCD of each side 1000 km. Its speed along AB is 250 kmh^-1, along BC 500 kmh^-1, along CD 200 kmh^-1 and along DA 100 kmh^-1. Its average speed (in kmh^-1)over the entire trip is

• 225.5

• 175.5

• 190.5

• 310.5

Free fall of an object (in vacuum) is a case of motion with

• uniform velocity

• uniform acceleration

• variable acceleration

• constant momentum

The position of a particle is given by $\overrightarrow{\mathrm{r}} = 2{\mathrm{t}}^2 \hat{\mathrm{i}} + 3\mathrm{t} \hat{\mathrm{j}} + 4 \hat{\mathrm{k}}$, where t is in second and the coefficients have proper units for $\overrightarrow{\mathrm{r}}$ to be in metre. The $\overrightarrow{\mathrm{a}} \left(\mathrm{t}\right)$ of the particle at t = 1 s is

• 4 ms^-2 along y-direction

• 3 ms^-2 along x-direction

• 4 ms^-2 along x-direction

• 2 ms^-2 along z-direction

A body is falling freely under gravity. The distances covered by the body in first, second and third minute of its motion are in the ratio

• 1 : 4 : 9

• 1 : 2 : 3

• 1 : 3 : 5

• 1 : 5 : 6