Speed-time graph: (0, 0) (3, 15) (9, 15) (12, 0), find the…

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) (3, 15) (9, 15) (12, 0), find the acceleration of each part.

speed-time graph: (0, 0) (3, 15) (9, 15) (12, 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 15 in 3 s.

15/3 is 5.

A: acceleration = 153 = 5 m/s²

Part B is flat: the speed stays the same.

The acceleration is 0.

B: acceleration = 06 = 0 m/s²

Part C: the speed goes down by 15 in 3 s.

-15/3 is −5.

Negative: it is slowing down, a deceleration.

C: acceleration = −153 = −5 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!

5 × 3 = 15, −5 × 3 = −15

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) (3, 30) (9, 30) (12, 0)

Show the answer

A: 10 m/s², B: 0 m/s², C: −10 m/s²