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

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. $\frac{2v}{a}$

2. $\frac{v}{a}$

3. $\frac{v}{2a}$

4. $\sqrt{\frac{v}{2a}}$ 

A particle moves along X-axis in such a way that its coordinate X varies with time t according to the equation $x=(2-5t+6t^2)m$. The initial velocity of the particle is 

1. –5 m/s

2. 6 m/s

3. –3 m/s

4. 3 m/s 

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. $\frac{aT}{4}$

2. $\frac{3aT}{2}$

3. $\frac{aT}{2}$

4. aT

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

If the velocity of a particle is given by \(v = (180-16x)^{1/2}~\text{m/s}\), then its acceleration will be: 

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. $a\propto t^2$

2. $a\propto t^4$

3. $a\propto t^3$

4. $a\propto t$ 

Starting from rest, acceleration of a particle is $a=2(t-1).$ 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

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

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