A car travels 90 km east and then 30 km west along the same straight road. If the entire journey takes 3 hours, what is the average velocity of the car?
20 km/h east
The problem requires us to calculate the average velocity of a car that first travels 90 km east and then 30 km west along the same road. The total time taken for this journey is 3 hours. We need to find the average velocity, which is different from average speed because velocity is a vector quantity and it considers the direction.
Let's solve the problem step-by-step:
- The car travels 90 km east, which we will consider as positive direction. Therefore, the displacement for this leg of the journey is +90 km.
- Next, the car travels 30 km west, which is in the opposite direction. We consider this as negative, so the displacement for this leg is -30 km.
- The total displacement is calculated as the sum of the individual displacements. Therefore, the total displacement = +90 km + (-30 km) = +60 km.
- The total time taken for the journey is 3 hours.
- The average velocity is given by the formula:
- Substituting the known values, we get:
- The positive sign indicates the direction is east. Therefore, the average velocity of the car is 20 km/h east.
Therefore, the correct option is: 20 km/h east.
The other options can be ruled out since they either suggest a different speed or the wrong direction. For instance, 50 km/h north is incorrect as there's no component of the journey in the north direction. The calculation confirms that 20 km/h east is the correct answer.
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