Velocity-Time Graphs: Slope and Area

Lesson 6 of 10 · 7 min · Free, no account needed

What you will learn

A velocity-time graph puts time across and speed up.
Its slope is the acceleration: how many m/s are added each second.
The area under it is the distance. A cell of 1 s × 1 m/s is 1 m. A triangle from rest is half the rectangle.

Your phone only knows your speed once a second. Can it still tell how far you went?
This car holds 10 m/s for 5 s. Drag the flag to where it ends up.
Watch the area under the line fill as the car drives.
Each cell is 1 s wide and 1 m/s tall.
Now the car pulls away from rest. Drag the start of the line down to 0.
Watch the shaded area: how much of the dashed block is left?
Two things to read on a velocity-time graph.
A velocity-time graph: time across, speed up.
Its slope is the acceleration: 8 m/s gained in 6 s is 8 ÷ 6 ≈ 1.3 m/s².
The area under it is the distance: half of 6 × 8 = 24 m. Simplified: this works for straight-line motion that does not turn back.
Plan a 12 s drive that covers exactly 100 m.
Draw the speed. The shaded area counts the metres. Then the car drives your plan.
Tap the piece where the car speeds up the hardest.
That is the biggest acceleration.
Game: parking pro. Three bays.
Shape the speed graph so the car stops inside each bay. Count the cells first, then press Go.
From math: the speed graph is a curve now. Strips can still count the area.
Try 1 s strips and ¼ s strips. Pick the one closer to how far the car really goes.
A car goes from 0 to 20 m/s in 4 s, speeding up evenly. How far does it go?
Find the area of the triangle.
Your 100 m plan, driven one more time.
Press Play.

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