A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is

(1) 4.0 m/s

(2) 5.0 m/s

(3) 5.5 m/s

(4) 4.8 m/s

Concept Questions :-

Average speed and average velocity
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Difficulty Level:

The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity v0 The distance travelled by the particle in time t will be

(1) ${v}_{0}t+\frac{1}{3}b{t}^{2}$

(2) ${v}_{0}t+\frac{1}{3}b{t}^{3}$

(3) ${v}_{0}t+\frac{1}{6}b{t}^{3}$

(4) ${v}_{0}t+\frac{1}{2}b{t}^{2}$

Concept Questions :-

Non-uniform acceleration
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A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be

1. 110 m/s

2. 55 m/s

3. 550 m/s

4. 660 m/s

Concept Questions :-

Graphs
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A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is

(1) $\left(\frac{{\alpha }^{2}+{\beta }^{2}}{\alpha \beta }\right)\text{\hspace{0.17em}}t$

(2) $\left(\frac{{\alpha }^{2}-{\beta }^{2}}{\alpha \beta }\right) t$

(3) $\frac{\left(\alpha +\beta \right)\text{\hspace{0.17em}}t}{\alpha \beta }$

(4) $\frac{\alpha \beta \text{\hspace{0.17em}}t}{\alpha +\beta }$

Concept Questions :-

Acceleration
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A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t1 and t2 seconds respectively, then

(1) $t={t}_{1}-{t}_{2}$

(2) $t=\frac{{t}_{1}+{t}_{2}}{2}$

(3) $t=\sqrt{{t}_{1}{t}_{2}}$

(4) $t={t}_{1}^{2}{t}_{2}^{2}$

Concept Questions :-

Uniformly accelerated motion
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A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

(1) $\frac{v}{g}+\frac{2hg}{\sqrt{2}}$

(2) $\frac{v}{g}\left[1-\sqrt{1+\frac{2h}{g}}\right]$

(3) $\frac{v}{g}\left[1+\sqrt{1+\frac{2gh}{{v}^{2}}}\right]$

(4) $\frac{v}{g}\left[1+\sqrt{{v}^{2}+\frac{2g}{h}}\right]$

Concept Questions :-

Uniformly accelerated motion
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Difficulty Level:

A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of 1 m each will then be

(1) All equal, being equal to $\sqrt{2/g}$ second

(2) In the ratio of the square roots of the integers 1, 2, 3.....

(3) In the ratio of the difference in the square roots of the integers i.e. $\sqrt{1},\text{\hspace{0.17em}}\left(\sqrt{2}-\sqrt{1}\right),\text{\hspace{0.17em}}\left(\sqrt{3}-\sqrt{2}\right),\text{\hspace{0.17em}}\left(\sqrt{4}-\sqrt{3}\right)$ ....

(4) In the ratio of the reciprocal of the square roots of the integers i.e.,. $\frac{1}{\sqrt{1}},\text{\hspace{0.17em}}\frac{1}{\sqrt{2}},\frac{1}{\sqrt{3}},\text{\hspace{0.17em}}\frac{1}{\sqrt{4}}$

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A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (Given $g=9.8m/{s}^{2}\right)$

(1) At least 0.8 m/s

(2) Any speed less than 19.6 m/s

(3) Only with speed 19.6 m/s

(4) More than 19.6 m/s

Concept Questions :-

Acceleration
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Difficulty Level:

If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is

(1) $\frac{1}{2}g{t}^{2}$

(2) $ut-\frac{1}{2}g{t}^{2}$

(3) $\left(u-gt\right)t$

(4) $ut$

Concept Questions :-

Uniformly accelerated motion
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Difficulty Level:

The variation of velocity of a particle with time moving along a straight line is illustrated in the following figure. The distance travelled by the particle in four seconds is

1. 60 m

2. 55 m

3. 25 m

4. 30 m

Concept Questions :-

Graphs