A boat is moving with velocity of $3\hat{i}+4\hat{j}$ in river and water is moving with a velocity of $-3\hat{i}-4\hat{j}$ with respect to ground. Relative velocity of boat with respect to water is: 

1. $-6\hat{i}-8\hat{j}$

2. $6\hat{i}+8\hat{j}$

3. $8\hat{j}$

4. $6\hat{i}$

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

An express train is moving with a velocity v₁. Its driver finds another train is moving on the same track in the same direction with velocity v₂. To escape collision, driver applies a retardation 'a' on the train. The minimum time of escaping collision will be 

1.  $t=\frac{v_1-v_2}{a}$
2.  $t_1=\frac{v_1^2-v_2^2}{2}$
3.  None
4.  Both

A stone falls from a balloon that is descending at a uniform rate of 12 m/s. The displacement of the stone from the point of release after 10 sec is

1. 490 m

2. 510 m

3. 610 m

4. 725 m

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 body A is projected upwards with a velocity of 98 m/s. The second body B is projected upwards with the same initial velocity but after 4 sec. Both the bodies will meet after

1. 6 sec

2. 8 sec

3. 10 sec

4. 12 sec

Two bodies of different masses m_a and m_b are dropped from two different heights a and b. The ratio of the time taken by the two to cover these distances are 

1. a : b

2. b : a

3. $\sqrt{a}:\sqrt{b}$

4. $a^2:b^2$

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of 

1. 3 s

2. 5 s

3. 7 s

4. 9 s

A stone is dropped into water from a bridge 44.1 m above the water. Another stone is thrown vertically downward 1 sec later. Both strike the water simultaneously. What was the initial speed of the second stone?

1. 12.25 m/s

2. 14.75 m/s

3. 16.23 m/s

4. 17.15 m/s

A body is released from a great height and falls freely towards the earth. Another body is released from the same height exactly one second later. The separation between the two bodies, two seconds after the release of the second body is 

1. 4.9 m

2. 9.8 m

3. 19.6 m

4. 24.5 m