Distance and Displacement

Question

A car travels west for 45 kilometers. It then turns south for 60 kilometers. The entire trip took 2 hours. What is the magnitude and direction of the car's average velocity? What was the car's average speed?

Answer 1

distance is how far you go: In this case 60 km + 45 km = 105 km (odometer reading)

displacement is far you end up with respect to where you started (This is obtained from the vector sum of the two displacements). Because the vectors are at right angles, we can use Pythagorean Theorem to find the resultant vector magnitude: sqrt( 45² + 60²) = 75 km (It's a 3-4-5 triangle). In order to find the math angle (CCl from East) we can use θ = tan^-1(d_y/d_x) (+ 180 if d_x < 0). To do this we must use the appropriate sign for d_x and d_y (W is negative and S is negative) θ = tan^-1(-45/-60) + 180 = 216.87°.

The average speed magnitude = total distance/time

The average velocity magnitude =total displacement/time in the direction of the total displacement

(you can give the math angle 216.87 as 36.87° South of West.)