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 |
 74%
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A body A moves with a uniform acceleration a and zero initial velocity. Another body B, starts from the same point moves in the same direction with a constant velocity v. The two bodies meet after a time t. The value of t is 

1. 2va

2. va

3. v2a

4. v2a 

Subtopic:  Uniformly Accelerated Motion |
 66%
From NCERT
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A particle moves along X-axis in such a way that its coordinate X varies with time t according to the equation x=(25t+6t2)m. The initial velocity of the particle is 

(1) –5 m/s

(2) 6 m/s

(3) –3 m/s

(4) 3 m/

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 88%
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A car starts from rest and moves with uniform acceleration 'a' on a straight road from time t = 0 to t = T. After that, a constant deceleration brings it to rest. In this process the average speed of the car is: 

(1) aT4

(2) 3aT2

(3) aT2

(4) aT

Subtopic:  Uniformly Accelerated Motion |
 58%
From NCERT
PMT - 2004
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An object accelerates from rest to a velocity of 27.5 m/s in 10 sec . Then find the distance covered by the object in the next 10 sec:

(1) 550 m

(2) 137.5 m

(3) 412.5 m

(4) 275 m

Subtopic:  Uniformly Accelerated Motion |
 58%
From NCERT
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If the velocity of a particle is given by \(v = (180-16x)^{1/2}~\text{m/s}\), then its acceleration will be: 

1. zero 2. \(8\) m/s2
3. \(-8\) m/s2 4. \(4\) m/s
Subtopic:  Acceleration |
 68%
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The displacement of a particle is proportional to the cube of time elapsed. How does the acceleration of the particle depends on time obtained 

(1) at2

(2) at4

(3) at3

(4) at 

Subtopic:  Acceleration |
 80%
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Starting from rest, acceleration of a particle is a=2(t1). The velocity of the particle at t=5s is:

1.  15 m/sec
2.  25 m/sec
3.  5 m/sec
4.  None of these

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 77%
From NCERT
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Speed of two identical cars are u and 4u at a specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is:

(1) 1 : 1

(2) 1 : 4

(3) 1 : 8

(4) 1 : 16

Subtopic:  Acceleration |
 78%
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A body is moving with uniform acceleration describes 40 m in the first 5 sec and 65 m in the next 5 sec. Its initial velocity will be:

(1) 4 m/s

(2) 2.5 m/s

(3) 5.5 m/s

(4) 11 m/s 

Subtopic:  Uniformly Accelerated Motion |
 69%
From NCERT
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