A car is travelling in a straight line at ??t =0?? at a speed of ??u?? m/s. The car has a constant positive acceleration. After 20 seconds the car has covered 400 m and is travelling at 30 m/s. Find ??u??.

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We know that the acceleration is constant and that we are travelling in a straight line, so we can use the 'suvat' equations to solve this question.
Remember that if ??s?? is displacement, ??u?? is initial velocity, ??v?? is final velocity, ??a?? is acceleration and ??t?? is time, then there are 5 equations that you should know:
$$v = u + at$$
$$s = ut + \frac{1}{2}at^{2}$$
$$s = \frac{1}{2}\left(u + v\right)t$$
$$v^{2} = u^{2} + 2as$$
$$s = vt - \frac{1}{2}at^{2}$$

In our problem we wish to find ??u?? and the variables that we know are:
$$ s = 400$$
$$ v = 30$$
$$t = 20$$

Therefore we need to use the 3rd equation in the list above and we can find our answer by substituting in values:
$$s = \frac{1}{2}\left(u + v\right)t$$
$$\implies 400 = \frac{1}{2}\left(u + 30\right)20$$
$$\implies 400 = \frac{u \times 20}{2} + \frac{30 \times 20}{2}$$
$$\implies 400 = 10u + 300$$
$$\implies 10u = 400 - 300$$
$$\implies 10u = 100$$
$$\implies u = 10$$

Therefore the car was initially travelling at 10 m/s.

This question is from Edexcel - Mechanics 1 - Motion In A Straight Line Under Constant Acceleration, why not try more questions
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