Mechanics - Motion Equations and Graphs

Scalar and Vector quantities

A scalar quantity only has magnitude. A vector quantity has magnitude and direction.

Scalar quantities

• distance
• speed
• mass
• volume
• energy
• power

Vector quantities

• displacement
• velocity
• acceleration
• force

Quantities

s= displacement or distance

u= initial velocity or speed

v= final velocity or speed

a= acceleration

t= time taken

Equations for uniform acceleration

v=u+at

s=ut+1/2 a t^2

v^2= u^2 +2as

Making graphs of motion

Motion can be represented using graphs. Data can be collected using a motion sensor or light gates. This setup records displacement at regular intervals, and can be used to create displacement against time or velocity against time graphs.

Key words

Both methods will eliminate human error, so time or displacement will be measured more accurately. They also allow greater precision than stopwatches.The data will have improved validity and reliability.

Displacement-time graphs

The line is straight if object is moving with constant velocity. A curve shows that the object is accelerating.

Gradient of a displacement-time graph is change in displacement/change in time = velocity

Velocity-time graphs

Gradient of a velocity-time graph is the change in velocity/change in time = acceleration

The area under a velocity-time graph is the displacement.