# A drunkard walking in a narrow lane takes $$5$$ steps forward and $$3$$ steps backward, followed again by $$5$$ steps forward and $$3$$ steps backward, and so on. Each step is $$1$$ m long and requires $$1$$ s. There is a pit on the road $$13$$ m away from the starting point. The drunkard will fall into the pit after: 1. $$37$$ s 2. $$31$$ s 3. $$29$$ s 4. $$33$$ s

Subtopic:  Distance & Displacement |
62%
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The speed-time graph of a particle moving along a fixed direction is shown in the figure. Then the distance traversed by the particle between $$t=0$$ s to $$10$$ s is:

1. $$70$$ m
2. $$60$$ m
3. $$50$$ m
4. $$40$$ m

Subtopic:  Graphs |
90%
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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 |
53%
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The position-time $$(x\text-t)$$ 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 $$500~\text{km/h}$$ ejects its products of combustion at the speed of $$1500~\text{km/h}$$ relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?
1. $$1000~\text{km/h}$$
2. $$500~\text{km/h}$$
3. $$1500~\text{km/h}$$
4. $$2000~\text{km/h}$$


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 |
75%
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