Section 2.22 - Sample problem: initial and final velocity



		The mouse goes 11.8 meters in 3.14 seconds at a constant acceleration of 1.21 m/s². What is its velocity at the beginning and end of the 11.8 meters?

To solve this problem, list the known variables and the ones you are asked for. Since there are two unknown values, the initial and final velocity, you will need to use two equations to solve this problem.

Variables

	displacement	Δx = 11.8 m
	acceleration	a = 1.21 m/s²
	elapsed time	t = 3.14 s
	initial velocity	v_i
	final velocity	v_f

What is the strategy?

There are two unknowns, the initial and final velocities, so choose two equations that include these two unknowns and the values you do know.
Substitute known values and use algebra to reduce the two equations to one equation with a single unknown value.
Solve the reduced equation for one of the unknown values, and then calculate the other value.

Physics principles and equations

These two motion equations contain the known and unknown values, and no other values.

v_f = v_i + at

Δx = ½(v_i + v_f)t

Step-by-step solution

There are other ways to solve this problem. For example, you could use the equation

Δx = v_it + ½at²

to find the initial velocity from the displacement, acceleration, and elapsed time. Then you could use the equation v_f = v_i + at to solve for the final velocity.