The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval to ?
1. | \(x\left(t_2\right)=x\left(t_1\right)+v\left(t_1\right)\left(t_2-t_1\right)+\left(\frac{1}{2}\right) a\left(t_2-t_1\right)^2\) |
2. | \(\mathrm{v}\left(\mathrm{t}_2\right)=\mathrm{v}\left(\mathrm{t}_1\right)+\mathrm{a}\left(\mathrm{t}_2-\mathrm{t}_1\right)\) |
3. | \(x\left(t_2\right)=x\left(t_1\right)+v_{\text {average }}\left(t_2-t_1\right)+\left(\frac{1}{2}\right) a_{\text {average }}\left(t_2-t_1\right)^2\) |
4. | \(\mathrm{v}_{\text {average }}=\left(\mathrm{x}\left(\mathrm{t}_2\right)-\mathrm{x}\left(\mathrm{t}_1\right)\right) /\left(\mathrm{t}_2-\mathrm{t}_1\right)\) |
A man walks on a straight road from his home to a market \(2.5\) km away with a speed of \(5\) km/h. Finding the market closed, he instantly turns and walks back home with a speed of \(7.5\) km/h. What is the magnitude of the average velocity of the man over the interval of time \(0\) to \(30\) min?
1. \(6\) km/h
2. \(5\) km/h
3. \(5.6\) km/h
4. \(6.6\) km/h
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:
1. | \(-,-,+\) |
2. | \(+,-,+\) |
3. | \(-,+,+\) |
4. | \(+,+,-\) |
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