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 particle moves along a path \(ABCD\) as shown in the figure. The magnitude of the displacement of the particle from \(A\) to \(D\) is:

1. $(5+10\sqrt{2})$m
2. \(10\) m
3. $15\sqrt{2}$ m
4. \(15\) m

For the following acceleration versus time graph, the corresponding velocity versus displacement graph is:

1.		2.
3.		4.

A stone falls freely from rest from a height \(h\) and it travels a distance of \(\frac{9 h}{25}\) in the last second. The value of \(h\) is:

The initial velocity of a particle is \(u\) (at \(t=0\)) and the acceleration \(f\) is given by \(at\). Which of the following relation is valid?
1. \(v = u + a t^{2}\)
2. \(v = u + a \frac{t^{2}}{2}\)
3. \(v = u + a t\)
4. \(v= u\)

Which of the following four statements is false?

Two cars \(A\) and \(B\) are travelling in the same direction with velocities \(v_1\) and \(v_2\) \((v_1>v_2).\) When the car \(A\) is at a distance \(d\) behind the car \(B,\) the driver of the car \(A\) applied the brake producing uniform retardation \(a.\) There will be no collision when:
1. \(d < \frac{\left( v_{1} - v_{2} \right)^{2}}{2 a}\)

2. \(d < \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)

3. \(d > \frac{\left(v_{1} - v_{2}\right)^{2}}{2 a}\)

4. \(d > \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)

A particle moves a distance \(x\) in time \(t\) according to equation \(x = (t+5)^{-1}\). The acceleration of the particle is proportional to: