Question

In a race, a runner traveled 12 meters in 4.0 seconds as she accelerated uniformly from rest. The magnitude of the acceleration of the runner was

Answer 1

The runner is moving by uniformly accelerated motion, starting from rest (so, his initial velocity is zero). The law of motion of the runner is
$x(t) = \frac{1}{2} at^2$
where x(t) is the distance covered after time t, and a is the acceleration of the runner. By re-arranging the formula, we get
$a= \frac{2S}{t^2}$
We know the runner has covered a distance of S=12m in t=4.0 s, and if we plug these numbers into the equation, we find the acceleration of the runner: 
$a= \frac{2S}{t^2} = \frac{(2*12m)}{(4s)^2} =1.5 m/s^2$