Question

Two cars approach each other; both cars are moving westward, one at 35 m/s, the other at 28 m/s. a. What is the velocity of the first car relative to (in the frame of reference of) the second car? b. After they pass, will their relative velocity change?

Answer 1

Given:

The velocity of the first car is: u = 35 m/s

The velocity of the second car is: v = 28 m/s

To find:

a) The relative velocity of the first car with respect to the frame of reference of the second car

b) Change in the relative velocity of the cars

Step-by-step explanation:

a) As both cars are moving in the same direction westward, the relative velocity of these cars is given as the difference between their velocities.

For every one second, the first car covers a distance of 35 m while the second car covers a distance of 28 m. Thus, the velocity of the first car with respect to the frame of reference of the second car is determined as:

`\begin{gathered} V_r=35\text{ m/s}-28\text{ m/s} \\ \\ V_r=7\text{ m/s} \end{gathered}`

b) As both the cars are moving in the same direction with the velocity of the first one being greater than the velocity of the second one. For every one second, the first car will always be 7 m away from the second car for every one second. Thus, these cars will not cross each other and their relative velocity will remain the same.

Final answer:

a) The velocity of the first car with respect to the frame of reference of the second car is 7 m/s.

b) The relative velocity of the cars will not change.