Question

the graph above represents a car driving down a straight highway. what is the acceleration from 0 - 4 seconds?

Explanation:

Step1: Recall acceleration formula

Acceleration $a=\frac{\Delta v}{\Delta t}$, where $\Delta v$ is change in velocity and $\Delta t$ is change in time. For a position - time graph, velocity $v$ is the slope of the graph.

Step2: Calculate the slope (velocity)

The position - time graph is a straight line, so the velocity is constant. Using two points $(t_1,x_1)=(0,0)$ and $(t_2,x_2)=(4,20)$ on the graph, the slope $v=\frac{x_2 - x_1}{t_2 - t_1}=\frac{20 - 0}{4 - 0}=5$ m/s. Since the velocity is constant, the change in velocity $\Delta v = 0$ m/s from $t = 0$ s to $t=4$ s and $\Delta t=4 - 0 = 4$ s.

Step3: Calculate acceleration

$a=\frac{\Delta v}{\Delta t}=\frac{0}{4}=0$ m/s²

Answer:

$0$ m/s²