Daniel B. answered 09/16/21
A retired computer professional to teach math, physics
Let
s(t) be the car's position at time t,
a(t) be the car's acceleration at time t.
First consider the possibility that the car's acceleration is constant,
i.e., for all t, a(t) = A for some constant A.
Under the assumption of constant acceleration we can use the formula
s(t) = s(0) + At²/2
Since s(0) = 0, we can rewrite that as
A = 2s(t)/t².
We are given s(t) for t = 0.5, 1.0, 1.5, 2.0.
If you plug in those four points, you get
A = 0.8 m/s²
for each of the four points.
That means that constant A = 0.8 m/s² offers the best fit to the given data.