Assuming that the car is travelling at constant acceleration, follows the equation:
v = (v_in) + at
where v = velocity
v_in = initial velocity, (at t = 0)
a = acceleration
t = time
Given the conditions, v = 51 at t = 3, and v = 59 at t = 5
Eqn 1: 51 = (v_in) + a(3)
Eqn 2: 59 = (v_in) + a(5)
Solving for v_in and a (using a calculator)
v_in = 39
a = 4
therefore the equation for the motion of the car is:
v = 39 + 4t
This equation can be plotted using excel or wolframalpha.
