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. | \(\small{x\left(t_2\right)=x\left(t_1\right)+v_{\text {average }}\left(t_2-t_1\right)+\left(\frac{1}{2}\right) a_{\text {average }}\left(t_2-t_1\right)^2\small}\) |
4. | \(\mathrm{v}_{\text {average }}=\left(\mathrm{x}\left(\mathrm{t}_2\right)-\mathrm{x}\left(\mathrm{t}_1\right)\right) /\left(\mathrm{t}_2-\mathrm{t}_1\right)\) |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA 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 |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyThe 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. | \(+,+,-\) |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA 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 |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & Biology