# 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:  Average Speed & Average Velocity |
52%
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The figure gives the x-t plot of a particle executing a one-dimensional simple harmonic motion. Then the signs of position & velocity variables of the particle at t = -1.2 sec respectively are:

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
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The position-time $$(x-t)$$ graphs for two children $$A$$ and $$B$$ returning from their school O to their homes P and Q respectively are shown in the graph. Choose the incorrect statement.

 1 $$B$$ reaches home faster than $$A.$$ 2 $$B$$ overtakes $$A$$ on the road twice. 3 $$B$$ walks faster than $$A.$$ 4 $$A$$ lives closer to the school than $$B.$$

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
60%
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A jet airplane travelling at the speed of  ejects its products of combustion at the speed of  relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?

Subtopic:  Relative Motion in One Dimension |
55%
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A car moving along a straight highway with a speed of $$126$$ km/h is brought to a stop within a distance of $$200$$ m. How long does it take for the car to stop?
1. $$10.2$$ s

2. $$9.6$$ s

3. $$11.4$$ s

4. $$6.7$$ s

Subtopic:  Uniformly Accelerated Motion |
72%
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Two trains A and B of length $$400$$ m each are moving on two parallel tracks with a uniform speed of $$72$$ km/h in the same direction with A ahead of B. The driver of B decides to overtake A and accelerates by $$1$$ m/s2If after $$50$$ s, the guard of B just brushes past the driver of A, what was the original distance between them?
1. $$2000$$ m
2. $$2250$$ m
3. $$1200$$ m
4. $$1250$$
m

Subtopic:  Uniformly Accelerated Motion |
53%
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On a two-lane road, car A is travelling at a speed of $$36$$ kmh-1Two cars B and C approach car A in opposite directions with a speed of $$54$$ kmh-1 each. At a certain instant, when the distance AB is equal to AC, both being $$1$$ km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?
1. $$1$$ ms-2
2. $$5$$ ms-2
3. $$2$$ ms-2
4. $$3$$
ms-2

Subtopic:  Uniformly Accelerated Motion |
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A player throws a ball upwards with an initial speed of . What is the direction of acceleration during the upward motion of the ball?

 1 vertically downwards 2 vertically upwards 3 first upwards then downwards 4 none of the above
Subtopic:  Uniformly Accelerated Motion |
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A particle in one-dimensional motion:

 1 with zero speed at an instant may have non-zero acceleration at that instant. 2 with zero speed may have non-zero velocity. 3 with constant speed, must have non-zero acceleration. 4 with a positive value of acceleration must be speeding up.

Subtopic:  Acceleration |
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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:  Average Speed & Average Velocity |
62%
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