A particle starts from rest and moves in a straight line such that its velocity, v, at time t seconds is given by \(v = (3t^{2} - 2t) ms^{-1}\). Determine t...

A particle starts from rest and moves in a straight line such that its velocity, v, at time t seconds is given by \(v = (3t^{2} - 2t) ms^{-1}\). Determine the acceleration when t = 2 secs.

Answer Details

The acceleration of a particle is given by the derivative of its velocity with respect to time. So we differentiate the given equation for velocity to find the acceleration: $$a = \frac{dv}{dt} = \frac{d}{dt}(3t^2 - 2t) = 6t - 2$$ When t = 2 seconds, the acceleration is: $$a = 6(2) - 2 = 10 \text{ ms}^{-2}$$ Therefore, the correct option is: \(\mathbf{10 ms^{-2}}\).