Relative velocity in 1-D

You're walking along a road, heading west at 8 km/hr. A car is going by with velocity of 30 km/hr east. There is also a truck passing, traveling at 40 km/hr west.

How fast is the truck traveling relative to you?

  1. 48 km/hr west
  2. 32 km/hr west
  3. 32 km/hr east
  4. 48 km/hr east

















How fast is the car traveling relative to you?

How fast is the truck traveling relative to the car?

One way to look at it is this: in an hour, the truck will be 40 km west of where you are now, but you will be 8 km west, so the truck will be 32 km further west than you in an hour. Relative to you, then, the truck has a velocity of 32 km/hr west. Similarly, relative to the truck, you have a velocity of 32 km/hr east.

To find the velocity of other things relative to a particular observer, subtract the observer's velocity from all the other velocities.

Do this to find the velocity of the truck relative to you. Using a subscript Y for you, T for the truck, and G for the ground, we can say:

The velocity of the truck relative to you is vTY = vTG - vYG

This is often written as: vTY = vTG + vGY

If you flip the order of the subscripts the vector is reversed.

The velocity of the truck relative to the ground = vTG = 40 km/hr west

The velocity of you relative to the ground = vYG = 8 km/hr west

The velocity of the truck relative to you, vTY = vTG - vYG = +40 -8 = 32 km/hr west

Similarly, the velocity of the car relative to you is 38 km/hr east.

The velocity of the truck relative to the car is 70 km/hr west, and the velocity of the car relative to the truck is 70 km/hr east.