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. | \(0\) |
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 \(r\). |