Speed-time graph: (0, 4) (4, 12) (10, 12), find the distance

Step by step, with the reason for every step · Speed-time graphs · Algebra 1

Step by step

Question: the speed-time graph joins (0, 4) (4, 12) (10, 12), find the distance.

speed-time graph: (0, 4) (4, 12) (10, 12)

Across: the time.

Up: the speed, in m/s.

Going up: speeding up.

Flat: a steady speed.

Going down: slowing down.

The distance is the area under a speed-time graph.

Speed times time is a rectangle; a steady speed-up is half a rectangle.

distance = area under the graph

Under part A: a rectangle and a triangle.

4 × 4 + a half × 4 × 8: 32.

A: area = 4 × 4 + ½ × 4 × 8 = 32

Under part B: a rectangle, 6 across and 12 up.

6 times 12 is 72.

B: area = 6 × 12 = 72

Careful!

12 is the top speed, read off the graph.

The distance is the area under it.

Careful: not distance = 12 m ✗

All the parts together: 104 m.

distance = 32 + 72 = 104 m

Let's check: the average speed is 10.4 m/s.

That is between 0 and the top speed, 12.

So the answer makes sense!

average speed = 104 ÷ 10 ≈ 10.4 m/s: between 0 and 12

Let's look back.

First: read the graph.

Then: distance = area.

Then: add the areas.

Last: check.

Answer

distance = 32 + 72 = 104 m

Try this one yourself, then check:

speed-time graph: (0, 8) (4, 24) (10, 24)

Show the answer

distance = 208 m