# 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

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