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 $$\mathrm{v}\left(\mathrm{t}_2\right)=\mathrm{v}\left(\mathrm{t}_1\right)+\mathrm{a}\left(\mathrm{t}_2-\mathrm{t}_1\right)$$ 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 $$\mathrm{v}_{\text {average }}=\left(\mathrm{x}\left(\mathrm{t}_2\right)-\mathrm{x}\left(\mathrm{t}_1\right)\right) /\left(\mathrm{t}_2-\mathrm{t}_1\right)$$

Subtopic: Â Average Speed & Average Velocity |
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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

Subtopic: Â Average Speed & Average Velocity |
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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 $$+,+,-$$
Subtopic: Â Average Speed & Average Velocity |
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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

Subtopic: Â Average Speed & Average Velocity |
Â 72%
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