Chapter 3, Problem 1Q

One car travels due east at 40 km/h, and a second car travels north at 40 km/h. Are their velocities equal? Explain

Solution

To Determine:

Whether the two cars have same velocity or not.

Solution:

Their velocities are not equal.

Explanation:

Velocity is a vector quantity which means it has both magnitude as well as direction. Speed is a scalar quantity. The magnitude of velocity is the speed. The speed of the two cars is same but their direction is different.

Thetwo cars have the same speed, 40 km/h but they are going in different directions, their velocities are different. If one draws a Cartesian plane, the North would be pointing to the positive side of the y -axis and the East to the positive side of the x- axis.

The velocities can be represented as follows:

Car 1 is traveling in North direction.

  $v_{car1}=40\text{km/h}\text{<mover accent="true"><mo>j</mo><mo>^</mo></mover>}$

Car 2 is traveling in East direction.

  $v_{car2}=40\text{km/h}\text{<mover accent="true"><mo>i</mo><mo>^</mo></mover>}$

Conclusions:

As it can be seen, their magnitude is the same, but they are pointing in different directions; therefore, their velocities are not equal.