The $x-$ and y- coordinates of the particle at any time are $x=5t-2t^2$ and y = 10t, respectivley, where x and y are in meters and t in seconds. The acceleration of the particle at

t = 2s is

(1) 5 $m/s^2$

(2) -4 $m/s^2$

(3) -8 $m/s^2$

(4) 0

A ship A is moving Westwards with a speed of 10 km $h^{-1}$ and a ship B 100 km South of A, is moving Northwards with a speed of 10 km $h^{-1}$. The time after which the distance between them becomes shortest, is

(1) 5 h

(2) $5\sqrt{2} h$

(3) $10\sqrt{2} h$

(4) 0 h

A body is moving with velocity 30 m$s^{-1}$ towards east. After 10 s its velocity becomes 40 m$s^{-1}$ towards north. The average acceleration of the both is

(1) 5 m$s^{-2}$

(2) 1 m$s^{-2}$

(3) 7 m$s^{-2}$

(4) $\sqrt{7}$ m$s^{-2}$

A particle of mass m is projected with velocity v making an angle of $45°$ with the horizontal. When the particle lands on the ground level the magnitude of the change in its momentum will be

(1) zero

(2) 2 mv

(3) mv / $\sqrt{2}$

(4) mv$\sqrt{2}$

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude and direction of acceleration of the stone?

(1) ${\mathrm{\pi }}^2{\mathrm{ms}}^{-2}$ and direction along the tangent to the circle.

(2) ${\mathrm{\pi }}^2{\mathrm{ms}}^{-2}$ and direction along the radius towards the centre.

(3) $\frac{{\mathrm{\pi }}^2}{4}m{s}^{-2}$ and direction along the radius towards the centre.

(4) ${\mathrm{\pi }}^2{\mathrm{ms}}^{-2}$ and direction along the radius away from the centre.

If a vector $2\hat{i}+3\hat{j}+8\hat{k}$ is perpendicular to the vector $4\hat{j}-4\hat{i}+\alpha \hat{k}$ then the value of $\alpha$ is 

(1) -1

(2) $\frac{-1}{2}$

(3) $\frac{1}{2}$

(4) 1

A boat which has a speed of 5 km $h^{-1}$ in still water crosses a river of width 1 km along the shortest possible path in 15 min. The velocity of the river water in km $h^{-1}$ is

(1) 1

(2) 3

(3) 4

(4) $\sqrt{41}$

Two particles are projected with same initial velocities at an angle $30° and 60°$ with the horizontal. Then

(1) their heights will be equal

(2) their ranges will be equal

(3) their time of flights will be equal

(4) their ranges will be different

A person swims in a river aiming to reach exactly opposite point on the banks of a river. His speed of swimming is 0.5 m $s^{-1}$ at an angle $120°$ with the direction of flow of water. The speed of water in stream is -

(1) 1.0 m$s^{-1}$

(2) 0.5 m $s^{-1}$

(3) 0.25 m$s^{-1}$

(4) 0.43 m$s^{-1}$

If a unit vector is represented by $0.5\hat{i}+0.8\hat{j}+c\hat{k}$ the value of c is 

(1) 1

(2) $\sqrt{0.11}$

(3) $\sqrt{0.01}$

(4) 0.39