Calculating Average speed and velocity

Question

A student drove to the university from her home and noted that the odometer reading of her car increased by 14.0 km. The trip took 19.0 min. (For each answer, enter a number.)

(a)

What was her average speed in km/h?

 km/h

(b)

If the straight-line distance from her home to the university is 10.3 km in a direction 25.0° south of east, what was her average velocity in km/h?

 km/h

(c)

If she returned home by the same path 7 h 30 min after she left, what were her average speed and velocity in km/h for the entire trip?

average speed(c) average speed km/h average velocity(c) average velocity km/h

Answer 1

Average speed is defined as distance traveled divided by time taken. Thus, for question (a), you would divide the change in odometer reading (14.0 km) by the time interval (19 min) to get the average speed in km/min. Speed is a scalar quantity, so no direction is included.

Average velocity is defined as displacement divided by time taken. Displacement is a vector quantity that expresses both the straight line distance from start to finish and the direction. Here the 10.3 km is the magnitude of the displacement, and 25 degrees S of E is its direction. To obtain the average velocity, divide this displacement by the 19 minutes. Express the magnitude of the average velocity in km/min. The direction of the average velocity is the same as that of the displacement.

For part (c), the calculation of average speed is the same as in (a), except that the numbers change. Here the distance traveled is 19.0 + 19.0 = 38.0 km, and for the time taken you need to add 7 hours and 30 minutes, expressed in minutes. For the velocity in part (c), note that the displacement equals 0 (starting point and finishing are the same), so the average velocity is also 0.