text: A particle moving in a straight line covers half the distance with a speed of $$3~\text{m/s}$$. The other half of the distance is covered in two equal time intervals with speeds of $$4.5~\text{m/s}$$ and $$7.5~\text{m/s}$$ respectively. The average speed of the particle during this motion is: 1. $$4.0~\text{m/s}$$ 2. $$5.0~\text{m/s}$$ 3. $$5.5~\text{m/s}$$ 4. $$4.8~\text{m/s}$$
  
  Subtopic:  Average Speed & Average Velocity |
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  A stone dropped from a building of height h and reaches the earth after t seconds. From the same building, if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t1 and t2 seconds respectively, then:
  
  1. $t={t}_{1}-{t}_{2}$
  
  2. $t=\frac{{t}_{1}+{t}_{2}}{2}$
  
  3. $t=\sqrt{{t}_{1}{t}_{2}}$
  
  4. $t={t}_{1}^{2}{t}_{2}^{2}$
  
  Subtopic:  Uniformly Accelerated Motion |
  77%
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  The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in 6 seconds are, respectively, :
  
  1. 8 m, 16 m
  
  2. 16 m, 8 m
  
  3. 16 m, 16 m
  
  4. 8 m, 8 m
  
  Subtopic:  Graphs |
  78%
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  In the following graph, the distance travelled by the body in metres is:
  
   1 $$200$$ 2 $$250$$ 3 $$300$$ 4 $$400$$
  Subtopic:  Graphs |
  86%
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  Given below are two statements:
  
   Assertion (A): Position-time graph of a stationary object is a straight line parallel to the time axis. Reason (R): For a stationary object, the position does not change with time.
  
   1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 Both (A) and (R) are False.
  Subtopic:  Distance & Displacement |
  88%
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  The acceleration of a particle starting from rest varies with time according to the relation A = – aω2sinωt. The displacement of this particle at a time t will be:
  
  1. $-\frac{1}{2}\left({\mathrm{a\omega }}^{2}\mathrm{sin\omega t}\right){\mathrm{t}}^{2}$
  
  2. $\mathrm{a\omega sin\omega t}$
  
  3. $\mathrm{a\omega cos\omega t}$
  
  4. $\mathrm{asin\omega t}$
  
  Subtopic:  Non Uniform Acceleration |
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  A thief is running away on a straight road in a jeep moving with a speed of $$9$$ m/s. A policeman chases him on a motorcycle moving at a speed of $$10$$ m/s. If the instantaneous separation of the jeep from the motorcycle is $$100$$ m, how long will it take for the policeman to catch the thief?
  1. $$1$$ s
  2. $$19$$ s
  3. $$90$$ s
  4. $$100$$ s
  
  Subtopic:  Relative Motion in One Dimension |
  83%
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  A particle is projected upwards. The times corresponding to height h while ascending and while descending are t1 and t2 respectively. The velocity of projection will be:
  
  1. gt1
  
  2. gt2
  
  3. $g$ $\left({t}_{1}+{t}_{2}\right)$
  
  4. $\frac{g\left({t}_{1}+{t}_{2}\right)}{2}$
  
  Subtopic:  Uniformly Accelerated Motion |
  69%
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  A body starts to fall freely under gravity. The distances covered by it in the first, second and third second will be in the ratio:
  1. $$1:3:5$$
  2. $$1:2:3$$
  3. $$1:4:9$$
  4. $$1:5:6$$
  
  Subtopic:  Uniformly Accelerated Motion |
  86%
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  A student is standing at a distance of 50 metres from the bus. As soon as the bus begins its motion with an acceleration of 1 ms–2, the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is:
  
  1. 5 ms–1
  
  2. 8 ms–1
  
  3. 10 ms–1
  
  4. 12 ms–1
  
  Subtopic:  Uniformly Accelerated Motion |
  73%
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