Linear Motion Equations

By: Nahdir Austin

Acceleration (p 48-49)• Acceleration: the rate

of change of velocity with respect to time

• aavg = Δv/Δt = (vf –vi)/(tf-ti)

• Notice how this form looks similar to that of velocity (Δx/Δt)

• Just as the slope of x vs t is velocity, the slope of v vs t is acceleration

Quick math questions• A car can accelerate at a rate of

2m/s2. How long will it take for the car to reach a speed of 30 m/s?

• What is the rate of acceleration for a car that slows from 30 m/s to a stop in three seconds?

Variables of linear motion

• d = displacement (Δx)• t = time of travel (Δt)• a = rate of constant acceleration• vi = initial velocity• vf = final velocity

Definitions of linear motion

• vavg = Δx/Δt• aavg = Δv/Δt

Key Steps in Problem Solving

Identify what you are looking forIdentify what you know (state your variables)Identify the equation(s) you need from the variables you have (and don’t have)Rearrange equations to solve for the unknownFix any unit issuesPlug and chugCheck your units

Practice # 1• A car travelling at 10.0 m/s

accelerates at a rate of 2.5 m/s2 to a final velocity of 20. m/s. How long

does it take for this to occur?

Practice # 2• A plane must reach a speed of 100

m/s at take off. If it takes 10 seconds to get down the runway, how long does the runway have to

be?

Practice #3• Upon lift off, a rocket ship

accelerates at a rate of 1 m/s2. How fast is it travelling when it reaches a

height of 10,000 m?

Theory behind the labWe know: d = vit + ½ a t2

If you drop something, vi = 0, so the equation reduces to: d = ½ at2

If you rearrange with a on the left you geta = 2d/t2

This lets you find the acceleration of an object due to gravity!!

You can also determine the slope of a graph of v vs. t to get a. We will do this too.