A particle has initial velocity $(3\hat{i}+4\hat{j})$ and has acceleration $(0.4\hat{i}+0.3\hat{j})$. Its speed after 10 s is

(1) 10 units

(2) 7 units

(3) $7\sqrt{2}$ units

(4) 8.5 units

A particle covers half of its total distance with speed $v_1$ and the rest half distance with speed $v_2$. Its average speed during the complete journey is

(1) $\frac{v_1+v_2}{2}$

(2) $\frac{v_1{v}_2}{v_1+v_2}$

(3) $\frac{2v_1{v}_2}{v_1+v_2}$

(4) $\frac{v_1^2+v_2^2}{v_1^2+v_2^2}$

The motion of a particle along a straight line is described by equation $x=8+12t-t^3,$ where x is in metre and t in second. The retardation of the particle, when its velocity becomes zero, is

(1) 24 m $s^{-2}$

(2) zero

(3) 6 m $s^{-2}$

(4) 12 m $s^{-2}$

A stone falls freely under gravity. It covers distance $h_1,<mspace\; width="1em"></mspace>h_2<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>h_3$ in the first 5 s, the next 5 s and the next 5 s respectively. The relation between $h_1,<mspace\; width="1em"></mspace>h_2<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>h_3$ is

(1) $h_1=2h_2=3h_3$

(2) $h_1=\frac{h_2}{3}=\frac{h_3}{5}$

(3) $h_2=3h_1<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>h_3=3h_2$

(4) $h_1=h_2=h_3$

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other day, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be

(1) $\frac{t_1{t}_2}{t_2-t_1}$

(2)  $\frac{t_1{t}_2}{t_2+t_1}$

(3) $t_1-t_2$

(4) $\frac{t_1+t_2}{2}$

A bus is moving with a speed of 10 m $s^{-1}$ on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

(1) 40 m$s^{-1}$

(2) 25 m$s^{-1}$

(3) 10 m$s^{-1}$

(4) 20 m$s^{-1}$

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 s is $S_1$ and that covered in the first 20 s is $S_2$, then

(1) $S_2=3S_1$

(2) $S_2=4S_1$

(3) $S_2=S_1$

(4) $S_2=2S_1$

A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 m$s^{-1}$ to 20 m $s^{-1}$ while passing through a distance 135 m in t s. The value of t is

(1) 9

(2) 10

(3) 1.8

(4) 12

A particle shows distance-time curve as shown in the figure below. The maximum instantaneous velocity of the particle is around the point

(1) A

(2) B

(3) C

(4) D

Two bodies, A (of mass 1 kg) and B (of mass 3 kg), are dropped from heights of 16 and 25 m, respectively. The ratio of the time taken by them to reach the ground is

(1) $\frac{5}{4}$

(2) $\frac{12}{5}$

(3) $\frac{5}{12}$

(4) $\frac{4}{5}$