Displacement Formula

Displacement is the change in an object’s position from the origin. Displacement is a vector quantity and thus has both magnitude and direction.

Displacement = (final position) – (initial position) = change in position

D = X_f -X_i

D = displacement

X_f = final position

X_i = initial position

ΔX = short form for change in position

Displacement Formula Questions:

1) Jane leaves Seattle to visit Mary in Alaska. She travels 350 miles due North but then back-tracks South 125 miles to pick up a friend. What is Jane’s total displacement?

Answer: Jane’s initial position in Seattle is X_i= 0. Her final position X_f is the distance traveled N minus the distance South. We can now calculate displacement, D.

D = ΔX = (X_f – X_i)

D = (350 mi N – 125 mi S) – 0

D = 225 mi N

2) You throw the ball 25 feet North for your dog. Your dog catches the ball and takes it past you to your brother, who is standing 5 feet to the South of where you are. What is the displacement of the ball?

Answer: Your initial position with the ball is X_i = 0. Because displacement is a vector quantity, ‘direction’ is considered. X_f = (30 feet S – 25 feet N), so X_f = -5 feet S.

D = ΔX = (X_f – X_i)

D = (30 ft S – 25 ft S) – 0

D = 5 ft S of your initial position