The position vector of a particle $\stackrel{\to }{\mathrm{r}}$ as a function of time t (in seconds) is $\stackrel{\to }{\mathrm{r}}$ $=$ $\left(3\mathrm{t}\right)\stackrel{^}{\mathrm{i}}$ $+$ $\left(2{\mathrm{t}}^{2}\right)\stackrel{^}{\mathrm{j}}$ $\mathrm{m}$. The initial acceleration of the particle is:

1. 2 $\mathrm{m}/{\mathrm{s}}^{2}$

2. 3 $\mathrm{m}/{\mathrm{s}}^{2}$

3. 4 $\mathrm{m}/{\mathrm{s}}^{2}$

4. Zero

Subtopic:  Acceleration |
86%
From NCERT
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The $$x$$ and $$y$$ coordinates of the particle at any time are $$x=5 t-2 t^2$$ and $${y}=10{t}$$ respectively, where $$x$$ and $$y$$ are in meters and $$\mathrm{t}$$ in seconds. The acceleration of the particle at $$\mathrm{t}=2$$ s is:

 1 $$5\hat{i}~\text{m/s}^2$$ 2 $$-4\hat{i}~\text{m/s}^2$$ 3 $$-8\hat{j}~\text{m/s}^2$$ 4 $$0$$
Subtopic:  Acceleration |
81%
From NCERT
NEET - 2017
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A body is moving with a velocity of $$30$$ m/s towards the east. After $$10$$ s, its velocity becomes $$40$$ m/s towards the north. The average acceleration of the body is:
1. $$7 \mathrm{~m} / \mathrm{s}^2$$
2. $$\sqrt{7} \mathrm{~m} / \mathrm{s}^2$$
3. $$5 \mathrm{~m} / \mathrm{s}^2$$
4. $$1 \mathrm{~m} / \mathrm{s}^2$$

Subtopic:  Acceleration |
76%
From NCERT
AIPMT - 2011
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If the position of a particle varies according to the equations $$x= 3t^2$$${}^{}$, $$y =2t$$, and $$z= 4t+4$$, then which of the following is incorrect?

 1 Velocities in $$y$$ and $$z$$ directions are constant 2 Acceleration in the $$x\text-$$direction is non-uniform 3 Acceleration in the $$x\text-$$direction is uniform 4 Motion is not in a straight line
Subtopic:  Acceleration |
74%
From NCERT
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A particle is moving in the XY plane such that $$x = \left(t^2 -2t\right)$$ m, and $$y = \left(2t^2-t\right)$$ m, then:

 1 Acceleration is zero at t = 1 sec 2 Speed is zero at t = 0 sec 3 Acceleration is always zero 4 Speed is 3 m/s at t = 1 sec
Subtopic:  Acceleration |
71%
From NCERT
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A particle moves so that its position vector is given by $$r=\cos \omega t \hat{x}+\sin \omega t \hat{y}$$ where $$\omega$$ is a constant.  Based on the information given, which of the following is true?

 1 Velocity and acceleration, both are parallel to r. 2 Velocity is perpendicular to r and acceleration is directed towards the origin. 3 Velocity is not perpendicular to r and acceleration is directed away from the origin. 4 Velocity and acceleration, both are perpendicular to r.
Subtopic:  Acceleration |
70%
From NCERT
NEET - 2016
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A particle moves in space such that:
$$x=2t^3+3t+4;~y=t^2+4t-1;~z=2sin\pi t$$
where $$x,~y,~z$$  are measured in meters and $$t$$ in seconds. The acceleration of the particle at $$t=3$$ seconds will be:

 1 $$36 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$$ ms-2 2 $$36 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\pi \hat{\mathrm{k}}$$ ms-2 3 $$36 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}$$ ms-2 4 $$12 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}$$ ms-2

Subtopic:  Acceleration |
67%
From NCERT
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A particle is moving along a curve. Select the correct statement.

 1 If its speed is constant, then it has no acceleration. 2 If its speed is increasing, then the acceleration of the particle is along its direction of motion. 3 If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion. 4 If its speed is constant, its acceleration is perpendicular to its velocity.
Subtopic:  Acceleration |
68%
From NCERT
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A particle moving on a curved path possesses a velocity of 3 m/s towards the north at an instant. After 10 s, it is moving with speed 4 m/s towards the west. The average acceleration of the particle is-

 1 0.25 $\mathrm{m}/{\mathrm{s}}^{2}$, 37° south to east 2 0.25 $\mathrm{m}/{\mathrm{s}}^{2}$, 37° west to north 3 0.5 $\mathrm{m}/{\mathrm{s}}^{2}$, 37° east to north 4 0.5 $\mathrm{m}/{\mathrm{s}}^{2}$, 37° south to west

Subtopic:  Acceleration |
68%
From NCERT
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A particle is moving eastwards with velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is?

 1 Zero 2 $$\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^2$$ toward north-west 3 $$\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^2$$ toward north-east 4 $$\frac{1}{2} m / s^2$$  toward north-west

Subtopic:  Acceleration |
63%
From NCERT
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