Motion Equations for Problem Solving - Kinematics

Motion Equations for problem solving with constant acceleration

Warm-Up

Is the Acceleration Constant, Increasing or Zero?

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The idea for this game and graphic come from a great high school physics teacher named Kelly O'Shea.

Video Instruction

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When an object is moving at a constant acceleration we can use the following equations to find motion information.

(see Reference Table)

1. Average Velocity

V = (V_i + V_f)/2 or V = Δd/Δt

2. Acceleration

a = (V_f − V_i)/t

Cross multiply & Solve: at = (V_f − V_i)

Add V_i to both sides

V_f = V_i + at

3. Displacement

V = Δd/Δt

Take Equation 3 and solve for d

Δd = VΔt

Substitute Equation 1 into the previous equation

Δd = [(V_i + V_f)/2]Δt

Since V_f = V_i + at

Δd = [(V_i + (V_i + at))/2]Δt

Gather like terms and solve for d

Δd = V_it + ½at²

“30 Seconds with Mr. G” - Number 4, Mindpaint Channel

5 quick questions — pick an answer to see if you’re right.

1. The constant acceleration motion equations can be used only when...

2. A car's velocity goes from 4 m/s to 10 m/s with constant acceleration. What is its average velocity?

3. An object moving at 5 m/s accelerates at 3 m/s² for 4 s. What is its final velocity?

4. Starting from rest, an object accelerates at 2 m/s² for 5 s. How far does it travel?

5. You know Vi, a, and t and want the final velocity. Which equation fits best?