The figure gives the \((x\text-t)\) plot of a particle in a one-dimensional motion. Three different equal intervals of time are shown. The signs of average velocity for each of the intervals \(1,\) \(2\) & \(3,\) respectively are:

If a body travels some distance in a given time interval, then for that time interval, its:

A car moves from \(X\) to \(Y\) with a uniform speed \(v_u\) and returns to \(X\) with a uniform speed \(v_d.\) The average speed for this round trip is:
1. \(\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}\)
2. \(\sqrt{v_{u} v_{d}}\)
3. \(\frac{v_{d} v_{u}}{v_{d} + v_{u}}\)
4. \(\frac{v_{u} + v_{d}}{2}\)

A vehicle travels half the distance \(L\) with speed \(v_1\) and the other half with speed \(v_2,\) then its average speed is:
1. \(\frac{v_{1} + v_{2}}{2}\)
2. \(\frac{2 v_{1} + v_{2}}{v_{1} + v_{2}}\)
3. \(\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}\)
4. \(\frac{L \left(\right. v_{1} + v_{2} \left.\right)}{v_{1} v_{2}}\)

The coordinate of an object is given as a function of time by \(x = 7 t - 3 t^{2}\), where \(x\) is in metres and \(t\) is in seconds. Its average velocity over the interval \(t=0\) to \(t=4\) is will be:
1. \(5\) m/s
2. \(-5\) m/s
3. \(11\) m/s
​​​​​​​4. \(-11\) m/s

A passenger arriving in a new town wishes to go from the station to a hotel located \(10\) km away on a straight road from the station. A dishonest cabman takes him along a circuitous path \(23\) km long and reaches the hotel in \(28\) min. The average speed of the taxi is:
1. \(30\) km/h
2. \(49.3\) km/h
3. \(55.6\) km/h
4. \(60\) km/h

A particle moving in a straight line covers half the distance with a speed of \(3~\text{m/s}\). The other half of the distance is covered in two equal time intervals with speeds of \(4.5~\text{m/s}\) and \(7.5~\text{m/s}\) respectively. The average speed of the particle during this motion is:
1. \(4.0~\text{m/s}\)
2. \(5.0~\text{m/s}\)
3. \(5.5~\text{m/s}\)
4. \(4.8~\text{m/s}\)

A car is moving along a straight line, say OP in the figure. It moves from O to P in \(18\) s and returns from P to Q in \(6.0\) s. The average velocity and average speed of the car in going from O to P and back to Q respectively are:

1. \(10\) m/s & \(10\) m/s

2. \(20\) m/s & \(30\) m/s 

3. \(20\) m/s & \(20\) m/s

4. \(10\) m/s & \(20\) m/s

The position of an object moving along \(x\)-axis is given by \(x=a+bt^2\), where \(a=8.5\) m, \(b=2.5\) ${\mathrm{ms}}^{-2}$ and \(t\) is measured in seconds. Its average velocity between \(t=2.0\) s and \(t=4.0\) s is:
1. \(10\) m/s
2. \(15\) m/s
3. \(20\) m/s
4. \(25\) m/s