- 1(current)
Q. No.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 \(t_1\) to \(t_2?\)
| 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. | \({v}\left({t}_2\right)={v}\left({t}_1\right)+{a}\left({t}_2-{t}_1\right)\) |
| 3. | \(\small{x\left(t_2\right)=x\left(t_1\right)+v_{\text {average }}\left(t_2-t_1\right)+\left(\frac{1}{2}\right) a_{\text {average }}\left(t_2-t_1\right)^2\small}\) |
| 4. | \({v}_{\text {average }}=\left[{x}\left({t}_2\right)-{x}\left({t}_1\right)\right] /\left({t}_2-{t}_1\right)\) |
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 \(1,\) \(2\) and \(3,\) respectively are:
| 1. | \(-,-,+\) | 2. | \(+,-,+\) |
| 3. | \(-,+,+\) | 4. | \(+,+,-\) |
A passenger arriving in a new town wishes to go from the station to a hotel located \(10~\text{km}\) away on a straight road from the station. A dishonest cabman takes him along a circuitous path \(23~\text{km}\) long and reaches the hotel in \(28~\text{min}.\) The average speed of the taxi is:
1. \(30~\text{km/h}\)
2. \(49.3~\text{km/h}\)
3. \(55.6~\text{km/h}\)
4. \(60~\text{km/h}\)
- 1(current)
Q. No.
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