A vehicle travels half the distance with speed \(v\) and the remaining distance with speed \(2v\). Its average speed is:
1. \(\frac{3v}{4}\)
2. \(\frac{v}{3}\)
3. \(\frac{2v}{3}\)
4. \(\frac{4v}{3}\)

The figure given below shows the displacement and time, \((x\text -t)\) graph of a particle moving along a straight line:
           
The correct statement, about the motion of the particle, is:

A stone is thrown vertically downwards with an initial velocity of \(40\) m/s from the top of a building. If it reaches the ground with a velocity of \(60\) m/s, then the height of the building is: (Take \(g=10\) m/s²)
1. \(120\) m
2. \(140\) m
3. \(80\) m
4. \(100\) m

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:

A man throws some balls with the same speed vertically upwards one after the other at an interval of \(2\) seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given \(g = 9.8\) m/s²)

If a ball is thrown vertically upwards with speed \(u\), the distance covered during the last \(t\) seconds of its ascent is:
1. \(ut\)
2. \(\frac{1}{2}gt^2\)
3. \(ut-\frac{1}{2}gt^2\)
4. \((u+gt)t\)