The car travels from A to B

The car travels from A to B, and then from B to C, as shown in the figure. Determine the magnitude of the displacement of the car and the distance traveled.

The car travels from A to B

Image from: R. C. Hibbeler, K. B. Yap, and S. C. Fan, Mechanics for Engineers: Dynamics (SI Edition), 13th ed. Singapore: Pearson Education South Asia, 2013.


We can write the directions of travel by the car in Cartesian form. Assume point A is our origin. Therefore, we can write the following (we are creating a position vector from A to C):

\Delta r=\left\{2i-3j\right\} km

The displacement is then the magnitude of this vector:

r_{displacement}=\sqrt{(2)^2+(-3)^2}=3.6 km


The total distance traveled is simply the addition of lengths:

distance = 2 km + 3 km = 5 km


This question can be found in Engineering Mechanics: Dynamics (SI edition), 13th edition, chapter 12, question 12-77.

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