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 |
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AIPMT - 2011
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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 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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Which of the following statements is incorrect?

 1 The average speed of a particle in a given time interval cannot be less than the magnitude of the average velocity. 2 It is possible to have a situation $$\left|\frac{d\overrightarrow {v}}{dt}\right|\neq0$$ but $$\frac{d\left|\overrightarrow{v}\right|}{dt}=0$$ 3 The average velocity of a particle is zero in a time interval. It is possible that instantaneous velocity is never zero in that interval. 4 It is possible to have a situation in which $$\left|\frac{d\overrightarrow{v}}{dt}\right|=0$$ but $$\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0$$
Subtopic: Â Acceleration |
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