A particle moves along X-axis in such a way that its coordinate X varies with time t according to the equation $x=(2-5t+6t^2)m$. The initial velocity of the particle is 

(1) –5 m/s

(2) 6 m/s

(3) –3 m/s

(4) 3 m/s 

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 ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is 

(1) 2100 m/sec² downwards

(2) 2100 m/sec² upwards

(3) 1400 m/sec²

(4) 700 m/sec²

A ball of mass m₁ and another ball of mass m₂ are dropped from equal height. If time taken by the balls are t₁ and t₂ respectively, then 

1. $t_1=\frac{t_2}{2}$

2. $t_1=t_2$

3. $t_1=4t_2$

4. $t_1=\frac{t_2}{4}$ 

Velocity of a body on reaching the point from which it was projected upwards, is 

1. $v=0$

2. $v=2u$

3. $v=0.5u$

4. $v=-u$

From the top of a tower, a particle is thrown vertically downwards with a velocity of 10 m/s. The ratio of the distances, covered by it in the 3^rd and 2^nd seconds of the motion is (Take $g=10m/s^2$) 

1. 5 : 7  

2. 7 : 5

3. 3 : 6

4. 6 : 3

When a ball is thrown up vertically with velocity V₀, it reaches a maximum height of 'h'. If one wishes to triple the maximum height then the ball should be thrown with velocity

1. $\sqrt{3}{V}_o$

2. 3 V₀

3. 9 V₀

4. 3/2 V₀

A particle starts from rest. Its acceleration (a) versus time (t) graph is as shown in the figure. The maximum speed of the particle will be:

1. 110 m/s

2. 55 m/s

3. 550 m/s

4. 660 m/s 

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (Given $g=9.8m/s^2)$

(1) At least 0.8 m/s

(2) Any speed less than 19.6 m/s

(3) Only with speed 19.6 m/s

(4) More than 19.6 m/s

The variation of velocity of a particle with time moving along a straight line is illustrated in the following figure. The distance travelled by the particle in four seconds is 

1. 60 m

2. 55 m

3. 25 m

4. 30 m