Speed-time graph: (0, 0) (2, 8) (6, 8) (8, 0), find the acceleration…

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

Step by step

Question: the speed-time graph joins (0, 0) (2, 8) (6, 8) (8, 0), find the acceleration of each part.

speed-time graph: (0, 0) (2, 8) (6, 8) (8, 0)

Across: the time.

Up: the speed, in m/s.

Going up: speeding up.

Flat: a steady speed.

Going down: slowing down.

Acceleration is the speed gained each second: the change in speed divided by the time.

On the graph, it is the slope.

acceleration = change in speedtime

Part A: the speed goes up by 8 in 2 s.

8/2 is 4.

A: acceleration = 82 = 4 m/s²

Part B is flat: the speed stays the same.

The acceleration is 0.

B: acceleration = 04 = 0 m/s²

Part C: the speed goes down by 8 in 2 s.

-8/2 is −4.

Negative: it is slowing down, a deceleration.

C: acceleration = −82 = −4 m/s²

Careful!

A slope going down gives a negative acceleration.

The object is slowing down.

Careful: going down = slowing down: negative

Let's check: acceleration times time gives back each change in speed.

So it is right!

4 × 2 = 8, −4 × 2 = −8

Let's look back.

First: read the graph.

Then: acceleration of each part.

Last: check.

Answer

Careful: going down = slowing down: negative

Try this one yourself, then check:

speed-time graph: (0, 0) (2, 12) (6, 12) (8, 0)

Show the answer

A: 6 m/s², B: 0 m/s², C: −6 m/s²