Question

Suppose a car begins at 100 kph, but decelerates at a rate of 20 km/h^2. Write a definite integral to represent the car's displacement during the first 4.5 hours and evaluate geometrically.

Answer 1

$$
u=100~kph\\
v=\cfrac{dx}{dt}\\
a=\cfrac{dv}{dt}\\
$$
If s is displacement, t is the time, u in initial velocity and a is acceleration, we get the following upon integrating the previous:
$$
s=ut+\cfrac{1}{2}at^2
$$
The question is asking you to get from the 1st set of equations to the displacement equation (i.e. s)

Geometrically, I would just draw an graph with distance (s) on the y axis and time (t) on the x axis, using the final equation.