A body is moving with a velocity of \(30~\text{m/s}\) towards the east. After \(10~\text s,\) its velocity becomes \(40~\text{m/s}\) 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:  Acceleration |
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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:  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:  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:  Acceleration |
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