A body starts from rest with uniform acceleration. If its velocity after n second is v, then its displacement in the last two seconds is

(1) $\frac{2v\left(n+1\right)}{n}$

(2) $\frac{v\left(n+1\right)}{n}$

(3) $\frac{v\left(n-1\right)}{n}$

(4) $\frac{2v\left(n-1\right)}{n}$

Concept Questions :-

Acceleration
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A point starts moving in a straight line with a certain acceleration. At a time t after beginning of motion the acceleration suddenly becomes retardation of the same value. The time in which the point returns to the initial point is

(1) $\sqrt{2t}$

(2) $\left(2+\sqrt{2}\right)\text{\hspace{0.17em}}t$

(3) $\frac{t}{\sqrt{2}}$

(4) Cannot be predicted unless acceleration is given

Concept Questions :-

Acceleration
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A particle is moving in a straight line and passes through a point O with a velocity of 6 ms–1. The particle moves with a constant retardation of 2 ms–2 for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O

(1) 3s

(2) 8s

(3) Never

(4) 4s

Concept Questions :-

Acceleration
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Difficulty Level:

A bird flies for 4 s with a velocity of $|\text{\hspace{0.17em}}t-2|\text{\hspace{0.17em}}m/s$ in a straight line, where t is time in seconds. It covers a distance of

1. 2 m

2. 4 m

3. 6 m

4. 8 m

Concept Questions :-

Distance and displacement
Graphs
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A particle is projected with velocity ${v}_{0}$ along x-axis. The deceleration of the particle is proportional to the square of the distance from the origin i.e., $a=\alpha {x}^{2}.$ The distance at which the particle stops is :

(1) $\sqrt{\frac{3{v}_{0}}{2\alpha }}$

(2) ${\left(\frac{3{v}_{o}}{2\alpha }\right)}^{\frac{1}{3}}$

(3) $\sqrt{\frac{3v{}_{0}{}^{2}}{2\alpha }}$

(4) ${\left(\frac{3v{}_{0}{}^{2}}{2\alpha }\right)}^{\frac{1}{3}}$

Concept Questions :-

Non-uniform acceleration
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A body is projected vertically up with a velocity v and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are

(1) $\stackrel{\to }{v}/2\text{\hspace{0.17em}}$ and v/2

(2) 0 and v/2

(3) 0 and 0

(4) $\stackrel{\to }{v}/2\text{\hspace{0.17em}}$ and 0

Concept Questions :-

Average speed and average velocity
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Difficulty Level:

A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4 h. The two stones cross each other after time

(1) $\sqrt{\frac{h}{8g}}$

(2) $\sqrt{8g\text{\hspace{0.17em}}h}$

(3) $\sqrt{2g\text{\hspace{0.17em}}h}$

(4) $\sqrt{\frac{h}{2g}}$

Concept Questions :-

Relative motion in 1-D
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Difficulty Level:

Four marbles are dropped from the top of a tower one after the other with an interval of one second. The first one reaches the ground after 4 seconds. When the first one reaches the ground the distances between the first and second, the second and third and the third and forth will be respectively

(1) 35, 25 and 15 m

(2) 30, 20 and 10 m

(3) 20, 10 and 5 m

(4) 40, 30 and 20 m

Concept Questions :-

Uniformly accelerated motion
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Difficulty Level:

A balloon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height h. The time taken by the stone to reach the ground is

(1) $4\sqrt{\frac{h}{g}}$

(2) $2\sqrt{\frac{h}{g}}$

(3) $\sqrt{\frac{2h}{g}}$

(4) $\sqrt{\frac{g}{h}}$

Concept Questions :-

Uniformly accelerated motion
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Difficulty Level:

Two bodies are thrown simultaneously from a tower with same initial velocity v0 : one vertically upwards, the other vertically downwards. The distance between the two bodies after time t is

(1) $2{v}_{0}t+\frac{1}{2}g\text{\hspace{0.17em}}{t}^{2}$

(2) 2v0t

(3) ${v}_{0}t+\frac{1}{2}g\text{\hspace{0.17em}}{t}^{2}$

(4) v0t

Concept Questions :-

Relative motion in 1-D