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 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

The distance between two particles is decreasing at the rate of \(6\) m/sec when they are moving in the opposite directions. If these particles travel with the same initial speeds and in the same direction, then the separation increases at the rate of \(4\) m/sec. It can be concluded that particles' speeds could be:
1. \(5\) m/sec, \(1\) m/sec
2. \(4\) m/sec, \(1\) m/sec
3. \(4\) m/sec, \(2\) m/sec
4. \(5\) m/sec, \(2\) m/sec

A man in a balloon rising vertically with an acceleration of $4.9m/{\sec }^2$ releases a ball 2 sec after the balloon is let go from the ground. The greatest height above the ground reached by the ball is $(g=9.8m/{\sec }^2)$  

1. 14.7 m

2. 19.6 m

3. 9.8 m

4. 24.5 m

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. $v=-u$

Time taken by an object falling from rest to cover the height of h₁ and h₂ is respectively t₁ and t₂ . Then the ratio of t₁ to t₂ is 

1. h₁ : h₂

2. $\sqrt{h_1}:\sqrt{h_2}$

3. h₁ : 2h₂

4. 2h₁ : h₂