A car passes a fixed point A at 10 ms $^{-1}$ and holds that velocity for $t_{1}$ seconds. It then accelerates uniformly over the next $t_{2}$ seconds until it reaches 15 ms $^{-1}$ .

Write down an expression for the magnitude of the car's acceleration during that stage, in terms of

t_{2}

Model answer

5/t2

Also accepted: 5/t_2, 5/(t2), 5 / t2

Explanation

On a velocity-time graph the gradient is the acceleration.

Over the accelerating stage the velocity rises from 10 ms $^{-1}$ to 15 ms $^{-1}$ , a change of 5 ms $^{-1}$ , and this takes $t_{2}$ seconds.

So the acceleration is $\dfrac{15-10}{t_{2}}=\dfrac{5}{t_{2}}$ ms $^{-2}$ .

Derived from ZIMSEC Mathematics 9164/4 Paper 4, June 2012, Q12

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