The motion of a particle is given by the equation $S=\left(3{t}^{3}+7{t}^{2}+14t+8\right)m,$ The value of the acceleration of the particle at t = 1 s is :

 1 10 m/s2 2 32 m/s2 3 23 m/s2 4 16 m/s2
Subtopic:  Acceleration |
93%
From NCERT
AIPMT - 2000
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A body is moving along a straight line according to the equation of motion, x$={\mathrm{t}}^{2}-3\mathrm{t}+4$, where x is in metre and t is in seconds. What is the acceleration of the body when it comes to rest?

1. Zero

2. $2$ $\mathrm{m}/{\mathrm{s}}^{2}$

3. $\frac{3}{2}$ $m/{s}^{2}$

4. $1$ $\mathrm{m}/{\mathrm{s}}^{2}$

Subtopic:  Acceleration |
84%
From NCERT
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The position $$x$$ of a particle varies with time $$t$$ as $$x=at^2-bt^3$$. The acceleration of the particle will be zero at time $$t$$ equal to:

 1 $$\dfrac{a}{b}$$ 2 $$\dfrac{2a}{3b}$$ 3 $$\dfrac{a}{3b}$$ 4 zero

Subtopic:  Acceleration |
84%
From NCERT
PMT - 1997
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A particle moves along a straight line such that its displacement at any time t is given by $\mathrm{S}={\mathrm{t}}^{3}-6{\mathrm{t}}^{2}+3\mathrm{t}+4$ metres. The velocity when the acceleration is zero is:

 1 4 ms-1 2 −12 ms−1 3 42 ms−1 4 −9 ms−1
Subtopic:  Acceleration |
81%
From NCERT
PMT - 1994
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The acceleration ‘a’ in m/s2 of a particle is given by $a=3{t}^{2}+2t+2$ where t is the time. If the particle starts out with a velocity, u = 2 m/s at t = 0, then the velocity at the end of 2 seconds will be:

1. 12 m/s

2. 18 m/s

3. 27 m/s

4. 36 m/s

Subtopic:  Acceleration |
72%
From NCERT
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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

Subtopic:  Acceleration |
67%
From NCERT
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When the velocity of a body is variable, then:

 1 its speed may be constant 2 its acceleration may be constant 3 its average acceleration may be constant 4 all of the above
Subtopic:  Acceleration |
70%
From NCERT
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A particle moves a distance $$x$$ in time $$t$$ according to equation $$x = (t+5)^{-1}$$. The acceleration of the particle is proportional to:

 1 $$(\text{velocity})^{\frac{3}{2}}$$ 2 $$(\text{distance})^2$$ 3 $$(\text{distance})^{-2}$$ 4 $$(\text{velocity})^{\frac{2}{3}}$$
Subtopic:  Acceleration |
65%
From NCERT
NEET - 2010
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A body is projected vertically in the upward direction from the surface of the earth. If the upward direction is taken as positive, then the acceleration of the body during its upward and downward journey is:

1. Positive, negative

2. Negative, negative

3. Positive, positive

4. Negative, positive

Subtopic:  Acceleration |
63%
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The velocity $$v$$ of an object varies with its position $$x$$ on a straight line as $$v=3\sqrt{x}.$$ Its acceleration versus time $$(a\text-t)$$ graph is best represented by:

 1 2 3 4
Subtopic:  Acceleration |
60%
From NCERT
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