Question 1

Paper 1Hard6 marks

A cart moves along a straight track. Figure 1 shows its signed acceleration, aa during the first 44 seconds. At t=0t=0 the cart has velocity 4 m s−14\text{ m s}^{-1} in the positive direction.

01234-6-4-20246t / sa / (m s-2)(0, -6)(2, 0)(4, 6)
(a)

Find an expression for the cart’s velocity, vv in terms of tt for 0≤t≤40\leq t\leq4

[2]
(b)

Find the total distance travelled by the cart during the first 44 seconds. Write down a suitable expression before evaluating it with your GDC, and give your answer to 3 significant figures.

[4]

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