Question

Starting from home, you bicycle 20 km north in 2.9 h, then turn around and pedal straight home in 1.9 h. What is your displacement after the first 2.9 h? What is your displacement for the entire trip? What is your average velocity for the entire trip?

Answer 1

Displacement after the first part: 20 km
Displacement for entire trip: 0 km
Average velocity: 0 m/s

Explanation:

Displacement tells you the distance between your starting point and your finish point.

If you break your trip into two stages, you have

• First part - you start at home and end up 20 km north;
• Second part - you start 20 km north and end up at home.

Now, before you start doing any calculations, you need to establish which direction is positive and which is negative. Let's assume that the direction that points away from your home is positive, and the direction that points towards your home, i.e. the opposite direction, is negative.

This means that, for the first part of the trip, your displacement is positive and equal to the distance you've travelled north

`d_1 = color(green)("20 km")`

To determine the displacement for your entire trip, you need to first figure out the displacement for the second part of the trip.

Since now you're moving towards your home, the displacement for this part will be negative

`d_2 = -"20 km"`

Therefore, the displacement for your entire trip will be

`d_"total" = d_1 + d_2`

`d_"total" = 20 + (-20) = color(green)("0 km")`

You start at home and end up at home, so your displacement is zero.

Average velocity is simply the ratio between the total displacement and the total time of travel. Since your displacement is zero, your average velocity will be zero as well

`bar(v) = d/t_"total" = "0 km"/((2.9 + 1.9)"h") = color(green)("0 km/h")`