Question

Your teacher's car can go from rest to 25 m/s (≈55 mph) in 10 seconds. The car's velocity changes at a uniform rate. Below is a quantitative velocity vs time graph that represents the motion of the car. Determine the acceleration of the car.

Answer 1

If the speed of the car changes uniformly, as shown in the graph, this means that the acceleration is constant. As the acceleration is the derivative of the speed

$a = \frac{\delta v}{\delta t}$

Then, this means that the acceleration is the slope of the equation of the line shown in the graph.

Then, we find the acceleration using the following equation:

$a = \frac{v_f- v_i}{t_2-t_1}\\\\a = \frac{25-0}{10}\\\\a = 2.5\ m/s ^ 2$

Then, the acceleration of the car is $2.5\ m/s^2$