Velocity and Speed

Mechanics Branch of physics that studies motion Two parts Kinematics – describes motion Dynamics – tells why motion occurs

Kinematics Translational Motion – motion without rotation All measurements must be made with respect to a frame of reference A man walks at 5 km/hr toward the front of a train traveling at 80 km/hr. What is the speed with respect to a) another passenger on the train b) a person standing outside the train? Unless otherwise stated the frame of reference is the earth

Vector Even distances need reference points Need to say how many km from what point Vector is a quantity that shows both a magnitude (amount) and a direction Represented by an arrow Scalar is a quantity that shows amount but not direction

Displacement vs Distance Displacement of an object is defined as a change in position – it is a vector Distance is not a vector A person walks 70m east and then turns around and walks 30m west a) what is the total distance traveled b) what is the displacement

Equation Displacement is the the ending position minus the starting position Δx = x 2 - x 1 A person starts at the +30 km mark and then walks to the +10 km mark, what is their displacement

Velocity vs Speed Velocity is a vector, speed a scalar Average speed – total distance divided by time Average velocity – total displacement divided by time Speed and velocity may or may not have the same magnitude

Example A person walks 70 m (E), then 30 m (W) in 70 sec. Find his a) speed b) velocity

Velocity Equation v = Δx/ Δt If v is +, moving to the right If v is -, moving to the left

Examples During a 3.00 s time interval a runners position changes from 50.0m to 30.5m. What is the average velocity over this time? How far can a cyclist travel in 2.5 hr along a straight road if her average velocity is 18km/hr?

Graphically Velocity can be shown graphically by plotting position vs time Slope of a position-time graph is velocity

Data for Car

Plot

Velocity is Slope 50m – 0m 5s – 0s V == 10m/s

Instantaneous Velocity If the graph is not a straight line, the velocity is constantly changing You can find the velocity at any specific point You do this by finding the slope of the line tangent to the curve

Changing Velocity Plot

What is Velocity at 3 Second? v (at 3s) = 4s – 2s 30m – 5m = 7.5m/s