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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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. $$\frac{a}{b}$$
2. $$\frac{2a}{3b}$$
3. $$\frac{a}{3b}$$
4. zero

Subtopic:  Acceleration |
84%
From NCERT
PMT - 1997
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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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A particle starting from rest undergoes a rectilinear motion with an acceleration $$a$$. The variation of acceleration with time $$t$$ is shown in the diagram. The final velocity of the object during its motion is:

1. $$6$$ m/s
2. $$16$$ m/s
3. $$24$$ m/s
4. $$12$$ m/s
Subtopic:  Acceleration |
83%
From NCERT
Hints

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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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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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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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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If a particle has negative velocity and negative acceleration, its speed:

 1 increases 2 decreases 3 remains the same 4 zero

Subtopic:  Acceleration |
66%
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