Formula

Relative speed: add when opposed, subtract when alike

Arithmetic • Time, Speed and Distance • Relative Speed

Formula

u + v if opposed, ∣ u - v ∣ if alike

Two bodies moving along the same line at speeds

u

and

v

approach or separate at

u + v

when their directions are opposite, and at

∣ u - v ∣

when their directions are the same.

How to use it

1Decide first whether the two directions agree; everything else follows from that single choice.
2Divide the gap that has to be closed by the relative speed to get the time.
3A stationary object has speed $0$ , so the relative speed is then the moving body's own speed.

Worked example

Two cars

180

km apart drive towards each other at

50

km/hour and

40

km/hour. When do they meet?

Step-by-step

1
They close at $50 + 40 = 90$ km/hour
Why: The directions are opposite, so the speeds add.
2
$\frac{180}{90} = 2$ hours

Answer

2

hours

Watch out

Both speeds must be in the same unit before they are combined. For same-direction motion at equal speeds the relative speed is zero, so the gap never closes at all.

Builds on

Speed, distance and time

Also known as

relative speed, opposite direction speeds add, same direction speeds subtract, closing speed

Appears in past papers

2020 (II)

Q38

2019 (I)

Formula

Worked example

Appears in past papers

2020 (II)

2019 (I)

2018 (II)

2018 (I)

2017 (I)

2016 (II)