# Displacement Formula

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 = Xf -Xi

D = displacement

Xf = final position

Xi = 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 Xi= 0. Her final position Xf is the distance traveled N minus the distance South. We can now calculate displacement, D.

D = ΔX = (Xf - Xi)

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 Xi = 0. Because displacement is a vector quantity, 'direction' is considered. Xf = (30 feet S - 25 feet N), so Xf = -5 feet S.

D = ΔX = (Xf - Xi)

D = (30 ft S - 25 ft S) - 0

D = 5 ft S of your initial position

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