The acceleration $$a$$ (in ${\mathrm{ms}}^{-2}$) of a body, starting from rest varies with time $$t$$ (in $$\mathrm{s}$$) as per the equation $$a=3t+4.$$ The velocity of the body at time $$t=2$$ $$\mathrm{s}$$ will be: 1. $$10$$ ${\mathrm{ms}}^{-1}$ 2. $$18$$ ${\mathrm{ms}}^{-1}$ 3. $$14$$ ${\mathrm{ms}}^{-1}$ 4. $$26$$ ${\mathrm{ms}}^{-1}$

Subtopic:  Non Uniform Acceleration |
72%
From NCERT
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A body thrown vertically so as to reach its maximum height in t second. The total time from the time of projection to reach a point at half of its maximum height while returning (in second) is:

1. $\sqrt{2}t$

2. $\left(1+\frac{1}{\sqrt{2}}\right)t$

3. $\frac{3t}{2}$

4. $\frac{t}{\sqrt{2}}$

Subtopic:  Uniformly Accelerated Motion |
57%
From NCERT
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A stone falls freely from rest from a height h and it travels a distance $\frac{9h}{25}$ in the last second. The value of h is:

1. 145 m

2. 100 m

3. 125 m

4. 200 ms

Subtopic:  Uniformly Accelerated Motion |
69%
From NCERT
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A point moves in a straight line under the retardation a${\mathrm{v}}^{2}$. If the initial velocity is $$\mathrm{u},$$ the distance covered in $$\mathrm{t}$$ seconds is:
1. $\mathrm{aut}$
2. $\frac{1}{\mathrm{a}}\mathrm{ln}$ $\left(\mathrm{aut}\right)$
3. $\frac{1}{\mathrm{a}}\mathrm{ln}$ $\left(1+\mathrm{aut}\right)$
4. $\mathrm{a}$ $\mathrm{ln}$ $\left(\mathrm{aut}\right)$

Subtopic:  Non Uniform Acceleration |
57%
From NCERT
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A particle is thrown upwards from ground. It experiences a constant resistance force which can produce retardation of 2 $m/{s}^{2}$. The ratio of time of ascent to the time of descent is:

(1) 1:1

(2) $\sqrt{\frac{2}{3}}$

(3) $\frac{2}{3}$

(4) $\sqrt{\frac{3}{2}}$

Subtopic:  Uniformly Accelerated Motion |
From NCERT
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A bullet loses $\frac{1}{20}$ of its velocity passing through a plank. The least number of planks required to stop the bullet is (All planks offers same retardation)

(1) 10

(2) 11

(3) 12

(4) 23

Subtopic:  Uniformly Accelerated Motion |
60%
From NCERT
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A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by $\left(4{t}^{3}-2t\right)$, where t is in sec and velocity in m/s. What is the acceleration of the particle, when it is 2 m from the origin ?

1. 28 m/s2

2. 22 m/s2

3. 12 m/s2

4. 10 m/s2

Subtopic:  Non Uniform Acceleration |
64%
From NCERT
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The relation between time and distance is given by $t=\alpha {x}^{2}+\beta x$, where α and β are constants. The retardation, as calculated based on this equation, will be (assume v to be velocity) :

1. $2\alpha {v}^{3}$

2. $2\beta {v}^{3}$

3. $2\alpha \beta {v}^{3}$

4. $2{\beta }^{2}{v}^{3}$

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
52%
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A point moves with uniform acceleration and v1, v2 and v3 denote the average velocities in the three successive intervals of time t1, t2 and t3. Which of the following relations is correct ?

(1) $\left({v}_{1}-{v}_{2}\right):\left({v}_{2}-{v}_{3}\right)=\left({t}_{1}-{t}_{2}\right):\left({t}_{2}+{t}_{3}\right)$

(2) $\left({v}_{1}-{v}_{2}\right):\left({v}_{2}-{v}_{3}\right)=\left({t}_{1}+{t}_{2}\right):\left({t}_{2}+{t}_{3}\right)$

(3) $\left({v}_{1}-{v}_{2}\right):\left({v}_{2}-{v}_{3}\right)=\left({t}_{1}-{t}_{2}\right):\left({t}_{1}-{t}_{3}\right)$

(4) $\left({v}_{1}-{v}_{2}\right):\left({v}_{2}-{v}_{3}\right)=\left({t}_{1}-{t}_{2}\right):\left({t}_{2}-{t}_{3}\right)$

Subtopic:  Uniformly Accelerated Motion |
51%
From NCERT
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The acceleration of a moving body can be found from:

(1) Area under the velocity-time graph

(2) Area under the distance-time graph

(3) Slope of the velocity-time graph

(4) Slope of the distance-time graph

Subtopic:  Graphs |
75%
From NCERT
PMT - 1981
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