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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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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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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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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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
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A body falls freely from the top of a tower. It covers 36% of the total height in the last second before striking the ground level. The height of the tower is

(1) 50 m

(2) 75 m

(3) 100 m

(4) 125 m

Concept Questions :-

Uniformly accelerated motion
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A particle is projected upwards. The times corresponding to height h while ascending and while descending are t1 and t2 respectively. The velocity of projection will be:

(1) gt1

(2) gt2

(3) $g\text{\hspace{0.17em}}\left({t}_{1}+{t}_{2}\right)$

(4) $\frac{g\left({t}_{1}+{t}_{2}\right)}{2}$

Concept Questions :-

Uniformly accelerated motion
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A projectile is fired vertically upwards with an initial velocity u. After an interval of T seconds a second projectile is fired vertically upwards, also with initial velocity u.

(1) They meet at time $t=\frac{u}{g}$ and at a height $\frac{{u}^{2}}{2g}+\frac{g{T}^{2}}{8}$

(2) They meet at time $t=\frac{u}{g}+\frac{T}{2}$ and at a height $\frac{{u}^{2}}{2g}+\frac{g{T}^{2}}{8}$

(3) They meet at time $t=\frac{u}{g}+\frac{T}{2}$ and at a height $\frac{{u}^{2}}{2g}-\frac{g{T}^{2}}{8}$

(4) They never meet

Concept Questions :-

Uniformly accelerated motion
Relative motion in 1-D
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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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