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 |
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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 |
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