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...
Question 1 Report
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: \(\mathbf{10 ms^{-2}}\).
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