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 = x2 - x1

• 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 – 0m5s – 0sV = = 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 – 2s30m – 5m = 7.5m/s