A train is moving in south with a speed of 90 ${\mathrm{kmh}}^{-1}$. The velocity of ground with respect to the train is:

1.  0 ${\mathrm{ms}}^{-1}$

2.  -25 ${\mathrm{ms}}^{-1}$

3.  25 ${\mathrm{ms}}^{-1}$

4.  -40 ${\mathrm{ms}}^{-1}$

 

Two parallel rail tracks run north-south. Train A moves north with a speed of 54 ${\mathrm{kmh}}^{-1}$, and train B moves south with a speed of 90 ${\mathrm{kmh}}^{-1}$. The magnitude of the velocity of B with respect to A is:

1.  40 ${\mathrm{ms}}^{-1}$

2.  0 ${\mathrm{ms}}^{-1}$

3.  25 ${\mathrm{ms}}^{-1}$

4.  15 ${\mathrm{ms}}^{-1}$

A train is moving in the north direction with a speed of \(54\) ${\mathrm{kmh}}^{-1}$. The velocity of a monkey running on the roof of the train against its motion (with a velocity of \(18\) ${\mathrm{kmh}}^{-1}$ with respect to the train) as observed by a man standing on the ground is:
1. \(40\) ms^-1
2. \(0\)
3. \(-5\) ms^-1
4. \(10\) ms^-1

The position of an object moving along the \(x\text-\)axis is given by, \(x=a+bt^2\), where \(a=8.5 ~\text m,\)  \(b=2.5~\text{m/s}^2,\) and \(t\) is measured in seconds. Its velocity at \(t=2.0~\text s\) will be:
1. \(13~\text{m/s}\) 
2. \(17~\text{m/s}\)
3. \(10~\text{m/s}\)
4. \(0~\text{m/s}\)

The position-time graph for a free-falling object is:

Figure shows x-t graph for a particle undergoing one-dimensional motion. What is the velocity of the particle at t=20 s?

1. 5 m/s

2. 10 m/s

3. Zero

4. 2 m/s

The figure shows the velocity-time graph for a particle. Acceleration in the time interval t=0 to t=8s will be:

1. Constant

2. Variable and decreasing with time

3. Variable and increasing with time

4. Can't say

The figure shows the velocity-time graph for a particle. What is the acceleration of the particle?

1. $\frac{v-v_o}{t_o}$

2. $\frac{v-2v_o}{t_o}$

3. $\frac{2v-v_o}{t_o}$

4. $\frac{v-v_o}{2t_o}$

Two figures shown below exhibit position-time graphs for particles undergoing one-dimensional motion. In which of the following graph(s), the acceleration of the particle is zero?

1. Only graph (a)

2. Only graph (b)

3. Both graphs (a) & (b)

4. Neither graph (a) nor (b)

A small block slides down on a smooth inclined plane starting from rest at time \(t=0.\) Let \(S_n\) be the distance traveled by the block in the interval \(t=n-1\) to \(t=n.\) Then the ratio \(\dfrac{S_n}{S_{n +1}}\) is: