# Exam-Style Question on Calculus

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 342. This question is similar to one that appeared on an IB Standard paper in 2018. The use of a calculator is allowed.

A particle P moves along a straight line. The velocity $$v$$ in metres per second of P after $$t$$ seconds is given by $$v(t) = 3\sin{t} - 8t^{\cos{t}}, 0 \le t \le 7$$.

(a) Find the initial velocity of P.

(b) Find the maximum speed of P.

(c) Write down the number of times that the acceleration of P is 0 ms-2.

(d) Find the acceleration of P at a time of 5 seconds.

(e) Find the total distance travelled by P.

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