The position vector of a particle $$\overrightarrow r$$ as a function of time $$t$$ (in seconds) is $$\overrightarrow r=3 t \hat{i}+2t^2\hat j~\text{m}$$. The initial acceleration of the particle is:
1. $$2~\text{m/s}^2$$
2. $$3~\text{m/s}^2$$
3. $$4~\text{m/s}^2$$

4. zero

Subtopic: Â Acceleration |
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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: Â Acceleration |
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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. $$7~\text{m/s}^2$$
2. $$\sqrt{7}~\text{m/s}^2$$
3. $$5~\text{m/s}^2$$
4. $$1~\text{m/s}^2$$

Subtopic: Â Acceleration |
Â 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: Â Acceleration |
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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: Â Acceleration |
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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: Â Acceleration |
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From NCERT
NEET - 2016
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A particle moves in space such that:
$$x=2t^3+3t+4;~y=t^2+4t-1;~z=2\sin\pi t$$
where $$x,~y,~z$$  are measured in meters and $$t$$ in seconds. The acceleration of the particle at $$t=3$$ seconds will be:

 1 $$36 \hat{i}+2 \hat{j}+\hat{k}$$ ms-2 2 $$36 \hat{i}+2 \hat{j}+\pi \hat{k}$$ ms-2 3 $$36 \hat{i}+2 \hat{j}$$ ms-2 4 $$12 \hat{i}+2 \hat{j}$$ ms-2
Subtopic: Â Acceleration |
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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 $$0.25~\text{m/s}^2,$$ $$37^{\circ}$$ south to east. 2 $$0.25~\text{m/s}^2,$$ $$37^{\circ}$$ west to north. 3 $$0.5~\text{m/s}^2,$$ $$37^{\circ}$$ east to north. 4 $$0.5~\text{m/s}^2,$$ $$37^{\circ}$$ south to west.

Subtopic: Â Acceleration |
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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: Â Acceleration |
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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 $$\frac{1}{\sqrt{2}}~ \text{m/s}^2$$ toward north-west 3 $$\frac{1}{\sqrt{2}}~\text{m/s}^2$$ toward north-east 4 $$\frac{1}{2}~\text{m/s}^2$$ toward north-west
Subtopic: Â Acceleration |
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