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

Concept Questions :-

Uniformly accelerated motion
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An object accelerates from rest to a velocity 27.5 m/s in 10 sec .Then find distance covered by object in next 10 sec

(1) 550 m

(2) 137.5 m

(3) 412.5 m

(4) 275 m

Concept Questions :-

Uniformly accelerated motion
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If the velocity of a particle is given by $v={\left(180-16x\right)}^{1/2}$m/s, then its acceleration will be

1. Zero

2. 8 m/s2

3. – 8 m/s2

4. 4 m/s

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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) $a\propto {t}^{2}$

(2) $a\propto {t}^{4}$

(3) $a\propto {t}^{3}$

(4) $a\propto t$

Concept Questions :-

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

Concept Questions :-

Instantaneous speed and instantaneous velocity
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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

Concept Questions :-

Acceleration
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A body is moving with uniform acceleration describes 40 m in the first 5 sec and 65 m in 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

Concept Questions :-

Uniformly accelerated motion
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The displacement x of a particle varies with time , where are positive constants. The velocity of the particle will

(1) Go on decreasing with time

(2) Be independent of $\alpha$ and $\beta$

(3) Drop to zero when $\alpha$ = $\beta$

(4) Go on increasing with time

Concept Questions :-

Instantaneous speed and instantaneous velocity
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A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance traversed is 15 S, then

(1) $S=\frac{1}{2}f{t}^{2}$

(2) $S=\frac{1}{4}f{t}^{2}$

(3) $S=\frac{1}{72}f{t}^{2}$

(4) $S=\frac{1}{6}f{t}^{2}$

Concept Questions :-

Acceleration
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A man is 45 m behind the bus when the bus starts accelerating from rest with acceleration of 2.5 m/s2. With what minimum velocity should the man start running to catch the bus?

1. 12 m/s

2. 14 m/s

3. 15 m/s

4. 16 m/s

Concept Questions :-

Relative motion in 1-D