A car is 2.0 km west of a traffic light at t = 0 and 5.0 km east of the light at t = 6.0 min. Assume the origin of the coordinate system is the light and the positive x direction is eastward. (a) What are the car's position vectors at these two times? (b) What is the car's displacement between 0 min and 6.0 min?

(a) Position Vectors V₁ = - 2î km, V₂=5î km

(b) Displacement Δx=7 km

Explanation:

Given data

Distance=2 km west at t=0

Distance=5 km east at t=6 min

Positive x is the east direction

To find

(a) Car position vector at given times

(b) Displacement between 0 to 6.0 min

Solution

For Part (a) car position vector at given times

At t=0 the distance=2 km west so conclude that x₁=-2 because it is in negative side So vector V₁

V₁ = - 2î km

At t=6.0 the distance=5 km east so conclude that x₂=5 because it is in positive side So vector V₂

V₂=5î km

For (b) displacement between 0 to 6.0 min

According to following mathematical law we can conclude that

Δx=x₂-x₁

Δx=5 - (-2) km

Δx=7 km