# 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: 567. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is allowed.

A particle moves in a straight line. During the first nine seconds the velocity, $$v$$ ms-1 of the particle at time $$t$$ seconds is given by:

$$v(t) = t \cos(t+5)$$

The following diagram shows the graph of v:

(a) Find the maximum value of $$v$$.

(b) Find the acceleration of the particle when t = 6.

(c) Find the total distance travelled by the particle.

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If you are using a TI-nSpire CX calculator and you would like to see an example of the process used in this question see Differentiation and Integration.

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