PHYA2 - Speed and Velocity

• Speed: the change in distance per unit time
• Velocity: the change in displacement per unit time
• Displacement: distance in a given direction

Motion at constant speed

• Speed v = s/t
• circle speed v=2  r/T where T is the time take to move round once
• Speed = gradient of a distance-time graph
• Velocity = gradient of displacement-time graph

Gradient of displacement-time graph = velocity, however acceleration is indicated by the curve

Acceleration: the change in velocity per unit time

Acceleration is a vector quantity, deceleration is negative 

The case of a ball thrown upwards is used below

• The ball reaches a maximum height (when velocity is instantaneously zero) then descends
• Intially the gradient is positive and large because as the ball leaves the hand the velocity is high
• As the ball rises the velocity decreases because it is acting against gravity
• As the ball descends the velocity increases due to gravity

Difference between distance-time and displacement time graphs

 Displacement-time graph

Distance-time graph

The case of a ball thrown upwards is used below

• The ball reaches a maximum height (when velocity is instantaneously zero) then descends
• Intially the gradient is positive and large because as the ball leaves the hand the velocity is high
• As the ball rises the velocity decreases because it is acting against gravity
• As the ball descends the velocity increases due to gravity

Velocity-time graphs

• Gradient represents acceleration
• Area beneath a velocity-time graph is displacement 
• The positive area represents displacement during ascent since upwards is considered positive
• The negative area represents displacement during descent since downward is considered negative