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11 June, 22:05

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?

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  1. 12 June, 00:58
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    (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
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