A particle moves along a straight line such that its displacement at any time \(t\) is given by \(S = t^{3} - 6 t^{2} + 3 t + 4\) metres. The velocity when the acceleration is zero is:

1. \(4\) ms-1 2. \(-12\) ms−1
3. \(42\) ms−1 4. \(-9\) ms−1

Subtopic:  Acceleration |
 81%
From NCERT
PMT - 1994
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If a body starts from rest and travels 120 cm in the 6th second, then what is the acceleration 

(1) 0.20 m/s2

(2) 0.027 m/s2

(3) 0.218 m/s2

(4) 0.03 m/s2

Subtopic:  Uniformly Accelerated Motion |
 80%
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If a car at rest accelerates uniformly to a speed of 144 km/h in 20 s. Then it covers a distance of 

(1) 20 m

(2) 400 m

(3) 1440 m

(4) 2880 m

Subtopic:  Uniformly Accelerated Motion |
 79%
From NCERT
PMT - 1997
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The position \(x\) of a particle varies with time \(t\) as \(x=at^2-bt^3\). The acceleration of the particle will be zero at time \(t\) equal to:

1. \(\dfrac{a}{b}\) 2. \(\dfrac{2a}{3b}\)
3. \(\dfrac{a}{3b}\) 4. zero
Subtopic:  Acceleration |
 85%
From NCERT
PMT - 1997
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If a train travelling at 72 kmph is to be brought to rest in a distance of 200 metres, then its retardation should be

(1) 20 ms–2

(2) 10 ms–2

(3) 2 ms–2

(4) 1 ms–2

Subtopic:  Uniformly Accelerated Motion |
 82%
From NCERT
PMT - 2004
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The displacement of a particle starting from rest (at t = 0) is given by s=6t2t3. The time in seconds at which the particle will attain zero velocity again, is  

(1) 2

(2) 4

(3) 6

(4) 8

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 80%
From NCERT
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Two cars A and B are at rest at the same point initially. If A starts with uniform velocity of 40 m/sec and B starts in the same direction with a constant acceleration of 4 m/s2, then B will catch A after how much time?

(1) 10 sec

(2) 20 sec

(3) 30 sec

(4) 35 sec

Subtopic:  Uniformly Accelerated Motion |
 58%
From NCERT
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The motion of a particle is described by the equation x=a+bt2 where a = 15 cm and b = 3 cm/s2. Its instantaneous velocity at time 3 sec will be 

(1) 36 cm/sec

(2) 18 cm/sec

(3) 16 cm/sec

(4) 32 cm/sec

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 90%
From NCERT
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A body is moving according to the equation x=at+bt2ct3 where x = displacement and a, b and c are constants. The acceleration of the body is 

(1) a+2bt 

(2) 2b+6ct 

(3) 2b6ct 

(4) 3b6ct2 

Subtopic:  Acceleration |
 90%
From NCERT
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A particle travels 10 m in first 5 sec and 10m in the next 3 sec. Assuming constant acceleration what is the distance travelled in next 2 sec ?

(1) 8.3 m

(2) 9.3 m

(3) 10.3 m

(4) None of above

Subtopic:  Uniformly Accelerated Motion |
From NCERT
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