Section 2.16 - Sample problem: velocity and acceleration



		The mouse car goes 10.3 meters in 4.15 seconds at a constant velocity, then accelerates at 1.22 m/s² for 5.34 more seconds. What is its final velocity?

Solving this problem requires two calculations. The mouse car's velocity during the first part of its journey must be calculated. Using that value as the initial velocity of the second part of the journey, and the rate of acceleration during that part, you can calculate the final velocity.

Draw a diagram

Variables

Part 1: Constant velocity

	displacement	Δx = 10.3 m
	elapsed time	Δt = 4.15 s
	velocity	v

Part 2: Constant acceleration

	initial velocity	v_i = v (calculated above)
	acceleration	a = 1.22 m/s²
	elapsed time	Δt = 5.34 s
	final velocity	v_f

What is the strategy?

Use the definition of velocity to find the velocity of the mouse car before it accelerates. The velocity is constant during the first part of the journey.
Use the definition of acceleration and solve for the final velocity.

Physics principles and equations

The definitions of velocity and acceleration will prove useful. The velocity and acceleration are constant in this problem. In this and later problems, we use the definitions for average velocity and acceleration without the bars over the variables.

v = Δx/Δt

a = Δv/Δt = (v_f − v_i)/Δt

Step-by-step solution