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 \(\frac{S_n}{S_{n +1}}\) is:
1. \(\frac{2n+1}{2n-1}\)
2. \(\frac{2n}{2n-1}\)
3. \(\frac{2n-1}{2n}\)
4. \(\frac{2n-1}{2n+1}\)

Train \(A\) and train \(B\) are running on parallel tracks in the opposite directions with speeds of \(36~\text{km/hour}\) and \(72~\text{km/hour}\), respectively. A person is walking in train \(A\) in the direction opposite to its motion with a speed of \(1.8~\text{km/hour}\). Speed (in ms^–1) of this person as observed from train \(B\) will be close to : (take the distance between the tracks as negligible)
1. \(30.5\) ms^–1
2. \(29.5\) ms^–1
3. \(31.5\) ms^–1
4. \(28.5\) ms^–1

A scooter accelerates from rest for time \(t_1\) at constant rate \(a_1\) and then retards at constant rate \(a_2\) for time \(t_2\) and comes to rest. The correct value of  \(\frac{t_1}{t_2}\) will be:
1. \(\frac{a_1+a_2}{a_2}\)
2. \(\frac{a_2}{a_1}\)
3. \(\frac{a_1}{a_2}\)
4. \(\frac{a_1+a_2}{a_1}\)

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)

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. $\frac{v-v_o}{2t_o}$

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

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 position-time graph for a free-falling object is:
1. a parabolic curve
2. a straight line
3. a circular curve
4. an elliptical curve

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

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