A body is moving with uniform acceleration describes 40 m in the first 5 sec and 65 m in the next 5 sec. Its initial velocity will be:

(1) 4 m/s

(2) 2.5 m/s

(3) 5.5 m/s

(4) 11 m/s 

The displacement x of a particle varies with time $t, x=a{e}^{-\alpha t}+b{e}^{\beta t}$, where $a,b,\alpha \text{\hspace{0.17em}and }\beta$ are positive constants. The velocity of the particle will 

1. Go on decreasing with time
2. Be independent of $\alpha$ and $\beta$
3. Drop to zero when $\alpha$ = $\beta$
4. Go on increasing with time

A car, starting from rest, accelerates at the rate f through a distance S, then continues at a constant speed for time t and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance traversed is 15 S, then, 

(1) $S=\frac{1}{2}f{t}^2$

(2) $S=\frac{1}{4}f{t}^2$

(3) $S=\frac{1}{72}f{t}^2$  

(4) $S=\frac{1}{6}f{t}^2$ 

A man is 45 m behind the bus when the bus starts accelerating from rest with acceleration of 2.5 m/s². With what minimum velocity should the man start running to catch the bus?

1.  12 m/s
2.  14 m/s
3.  15 m/s
4.  16 m/s

A particle moves along the x-axis as $\mathrm{x}=4(\mathrm{t}-2)+\mathrm{a}{(\mathrm{t}-2)}^2$. Which of the following is true? 

(1) The initial velocity of the particle is 4

(2) The acceleration of the particle is 2a

(3) The particle is at the origin at t = 0

(4) None of these

A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th sec to that covered in 5 sec is 

(1) 9/25

(2) 3/5

(3) 25/9

(4) 1/25

Two trains, each 50 m long, are travelling in the opposite direction with velocities 10 m/s and 15 m/s. The time of crossing is:

1. 10 sec

2. 4 sec

3. $2\sqrt{3}$ $\sec$

4. $4\sqrt{3}$ $\sec$

A 120 m long train is moving in a direction with speed 20 m/s. A train B moving with 30 m/s in the opposite direction and 130 m long crosses the first train in a time  

1.  4 s
2.  36 s
3.  38 s
4.  5 s

A 210-meter long train is moving due north at a speed of 25 m/s. A small bird is flying due South a little above the train with a speed of 5m/s. The time taken by the bird to cross the train is 

(1) 6 s

(2) 7 s

(3) 9 s

(4) 10 s

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

1.  150 m/s
2.  27 m/s
3.  450 m/s
4.  250 m/s