Maximizing Velocity Function Using Derivatives

00:00 3 marks

A car moves along a straight track such that its velocity \(v\) as a function of time \(t\) is given by \(v(t) = -4t^2 + 16t + 5\) m/s, where \(t\) is measured in seconds. Determine the maximum velocity attained by the car within the time interval \([0,6]\) seconds.

Hint Hint

Hint

To find the maximum velocity, first find the critical points by setting \(v'(t) = 0\), and then evaluate \(v(t)\) at these points and the endpoints of the interval.

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Answer Answer

Complete Answer

The maximum velocity is 21 m/s at \(t = 2\) seconds.

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