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. \(P,Q,R\)

A ball is dropped vertically from height \(h\) and bounces elastically on the floor (see figure). Which of the following plots best depicts the acceleration of the ball as a function of time?
                      

1.		2.
3.		4.

The accompanying graph of position \((x)\) versus time \((t)\) represents the motion of a particle. If \(p\) and \(q\) are both positive constants, the expression that best describes the acceleration of the particle is:
 

1. \(a=-p-qt\)

2. \(a=-p+qt\)

3. \(a=p+qt\)

4. \(a=p-qt\)

A man \((A)\) has to throw a ball vertically up to a partner \((B)\) who is standing up, above his level by \(15~\text{m}.\) The \((B)\) partner can catch the ball only when it comes downwards with a maximum speed of \(10~\text{m/s}\)
(take acceleration due to gravity as \(10~\text{m/s}^{2}\))
The minimum and maximum speeds of the throw are: (nearly)
1. \(10~\text{m/s}~\text{and}~20~\text{m/s}\)
2. \(10~\text{m/s}~\text{and}~30~\text{m/s}\)
3. \(20~\text{m/s}~\text{and}~20\sqrt{3}~\text{m/s}\)
4. \(10\sqrt{3}~\text{m/s}~\text{and}~20~\text{m/s}\)

A ball is thrown vertically upward and it reaches the highest point in \(4~\text s.\) Immediately, a second ball is thrown upwards with an initial speed that is twice that of the first. The second ball meets the first after a time:
1. \(1~\text s\) 
2. \(2~\text s\) 
3. \(3~\text s\)
4. \(4~\text s\)

A particle projected vertically under gravity passes a certain level on the way up at a time \(T_1\) and on the way down at a time \(T_2\) – after it was projected. The speed of projection is:

1. \(\dfrac{1}{2} g\left(T_{1}+T_{2}\right)\)

2. \(\dfrac{1}{2} g\left(T_{1}-T_{2}\right)\)

3. \(g \sqrt{T_{1} T_{2}}\)

4. \(\dfrac{1}{2} g \dfrac{T_{1} T_{2}}{T_{1}+T_{2}}\)

A boy throws a ball straight up the side of a building and receives it after \(4~\text s.\) On the other hand, if he throws it so that it strikes a ledge on its way up, it returns to him after \(3~\text s.\) The ledge is at a distance \(d\) below the highest point, where \(d=? \) (take acceleration due to gravity, \(g=10~\text{ms}^{-2})\)
1. \(5~\text m\)
2. \(2.5~\text m\)
3. \(1.25~\text m\)
4. \(10~\text m\)

A man driving a scooter at \(15~\text{m/s}\) brakes at the rate of \(2~\text{m/s}^2\). His speed, after \(10~\text{s}\) after the application of brakes will be:
1. \(5~\text{m/s}\)
2. \(-5~\text{m/s}\)
3. \(0~\text{m/s}\)
4. \(10~\text{m/s}\)