Motion in One Dimension

Motion in One Dimension x t v t a Honors Physics Lecture Notes t

ConcepTest 2.1 Walking the Dog You and your dog go for a walk to the park. On the way, your dog takes many side trips to chase squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the same displacement? 1) yes 2) no

ConcepTest 2.1 Walking the Dog You and your dog go for a walk to the park. On the way, your dog takes many side trips to chase squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the same displacement? 1) yes 2) no Yes, you have the same displacement. Since you and your dog had the same initial position and the same final position, then you have (by definition) the same displacement. Follow-up: Have you and your dog traveled the same distance?

Tuesday August 30th Introduction to 1-D Motion Distance versus Displacement

Kinematics • Kinematics is the branch of mechanics that describes the motion of objects without necessarily discussing what causes the motion. • 1-Dimensional Kinematics (or 1-Dimensional Motion) refers to motion in a straight line.

Distance • The total length of the path traveled by an object is called distance. • “How far have you walked?” is a typical question. • The SI unit of distance is the meter (m).

Displacement (x) • The change in the position of a particle is called displacement. • Δis a Greek letter used to represent the words “change in”. Δx therefore means “change in x”. It is always calculated by final value minus initial value. • “How far are you from home?” is a typical displacement question. • The SI unit for displacement is the meter (m). • Calculation of displacement:

Distance vs Displacement A 100 m displacement 50 m B distance • A picture can help you distinguish between distance and displacement.

Questions • Does the odometer in your car measure distance or displacement? Distance • Can you think of a circumstance in which it measures both distance and displacement? Yes, if the car moves in a straight line without backing up at all.

Practice Problem: Two tennis players approach the net to congratulate one another after a game. a) Find the distance and displacement of player A. b) Repeat for player B. A B 5 m 2 m • Distance = 5.0m Δx = +5.0 m because A moves in the positive direction. • Distance = 2.0 m Δx = -2.0 m because B moves in the negative direction.

Practice Problem: If Δx is the displacement of a particle, and d is the distance the particle traveled during that displacement, which of the following is always a true statement? a) b) c) d) e)

Practice Problem: You are driving a car on a circular track of diameter 40.0 meters. After you have driven around 21/2 times, how far have you driven, and what is your displacement? Begin with a drawing: distance is total length of path traveled. *distance = 2.5 (π) diameter = 2.5 (π) 40 m = 314 meters *displacement = Δx = 40m 40 m end start

Dx = xf- xi = -6 m - 5 m = -11 m DISPLACEMENT The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 0 2 4 6 Note:Motion to the left is negative

Dx = xf- xi = (-1 m) - (-6 m) = 5 m DISPLACEMENT The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 0 2 4 6 Note:Motion to the right is positive

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Motion in One Dimension