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 |
 69%
From NCERT
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The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity of v0. The distance travelled by the particle in time t will be:

(1) v0t+13bt2

(2) v0t+13bt3

(3) v0t+16bt3

(4) v0t+12bt2

Subtopic:  Non Uniform Acceleration |
 63%
From NCERT
PMT - 1995
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A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be: 

1. 110 m/s

2. 55 m/s

3. 550 m/s

4. 660 m/s 

Subtopic:  Graphs |
 72%
From NCERT
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A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is

1.  α2+β2αβt
2.  α2β2αβt
3.  (α+β)tαβ
4.  αβtα+β

Subtopic:  Uniformly Accelerated Motion |
 70%
From NCERT
PMT - 1994
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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=t1t2

2. t=t1+t22

3. t=t1t2

4. t=t12t22 

Subtopic:  Uniformly Accelerated Motion |
 77%
From NCERT
PMT - 1997
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A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

(1) vg+2hg2

(2) vg11+2hg

(3) vg1+1+2ghv2

(4) vg1+v2+2gh

Subtopic:  Uniformly Accelerated Motion |
 60%
From NCERT
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A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of 1 m each will then be:
1. All equal, being equal to \(\sqrt{2 / g} \) second. 
2. In the ratio of the square roots of the integers 1, 2, 3.....
3. In the ratio of the difference in the square roots of the integers \(\sqrt{1}\)\((\sqrt{2}-\sqrt{1})\),\((\sqrt{3}-\sqrt{2})\),\((\sqrt{4}-\sqrt{3})\) \( \ldots\)
4. In the ratio of the reciprocal of the square roots of the integers i.e... \(\frac{1}{\sqrt{1}}\)\(\frac{1}{\sqrt{2}}\)\(\frac{1}{\sqrt{3}}\),\(\frac{1}{\sqrt{4}} \)

Subtopic:  Uniformly Accelerated Motion |
 82%
From NCERT
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A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (Given g=9.8m/s2)

(1) At least 0.8 m/s

(2) Any speed less than 19.6 m/s

(3) Only with speed 19.6 m/s

(4) More than 19.6 m/s

Subtopic:  Acceleration |
 68%
From NCERT
PMT - 2003
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If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is 

(1) 12gt2

(2) ut12gt2

(3) (ugt)t

(4) ut

Subtopic:  Uniformly Accelerated Motion |
 58%
From NCERT
PMT - 2003
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The variation of velocity of a particle with time moving along a straight line is illustrated in the following figure. The distance travelled by the particle in four seconds is 

1. 60 m

2. 55 m

3. 25 m

4. 30 m

Subtopic:  Graphs |
 86%
From NCERT
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