A ball is thrown vertically upwards with a velocity \(u\) with respect to ground from a balloon descending with velocity \(v\) with respect to ground. The ball will pass the balloon after time:
1. \(\frac{u-v}{2g}\)
2. \(\frac{u+v}{2g}\)
3. \(\frac{2(u-v)}{g}\)
4. \(\frac{2(u+v)}{g}\)

The displacement time graph of a moving particle is shown in the figure below. The instantaneous velocity of the particle is negative at the point:

A ball is thrown vertically upwards. Then the velocity-time \((v\text-t)\) graph will be:

1.		2.
3.		4.

The graph of displacement time is given below.

Its corresponding velocity-time graph will be:

1.		2.
3.		4.

A car \(A\) is traveling on a straight level road at a uniform speed of \(60\) km/h. It is followed by another car \(B\) which is moving at a speed of \(70\) km/h. When the distance between them is \(2.5\) km, car \(B\) is given a deceleration of \(20\) km/h². After how much time will car \(B\) catch up with car \(A\)?
1. \(1\) hr
2. \(\frac{1}{2}\) hr
3. \(\frac{1}{4}\) hr
4. \(\frac{1}{8}\) hr

A ball is dropped vertically from a height \(h\) above the ground. It hits the ground and bounces up vertically to a height of \(\frac{h}{2}\). Neglecting subsequent motion and air resistance, its velocity \(v\) varies with the height \(h\) as:
[Take vertically upwards direction as positive.]

1.		2.
3.		4.

A particle moves along a straight line OX. At a time \(t\) (in seconds), the displacement \(x\) (in metres) of the particle from O is given by \(x= 40 +12t-t^3\). How long would the particle travel before coming to rest?

A car moves from \(X\) to \(Y\) with a uniform speed \(v_u\) and returns to \(X\) with a uniform speed \(v_d.\) The average speed for this round trip is:
1. \(\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}\)
2. \(\sqrt{v_{u} v_{d}}\)
3. \(\frac{v_{d} v_{u}}{v_{d} + v_{u}}\)
4. \(\frac{v_{u} + v_{d}}{2}\)

A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\) ms^-1 to \(20\) ms^-1 while covering a distance of \(135\) m in \(t\) seconds. The value of \(t\) is:

In the following displacement \((x)\) versus time \((t)\) graph, at which points \(P, Q\) and \(R\) will the object's speed be increasing?

1. \(R\) only
2. \(P\) only
3. \(Q\) and \(R\) only
4. \(P,Q,R\)