How Long to Overtake at Different Speeds?

[meredith]

Homework Statement

how long does it take a car traveling in the left lane at 60 km/h to overtake another car traveling in the right lane at 40 kn/h when the cars front bumpers are initially 100 m apart?

Homework Equations

relative velocity equations
V ab = v ae + V be

The Attempt at a Solution

i don't really know my work doesn't make sense and there's no sense typing it all in here cause its wrong and i can't even get al the symbols

 

[Rake-MC]

Relative to the 40km/h car, the car in the left lane is traveling 20km/h.

So now you have relative velocity, they give you relative distance (100m) solve for time.

Hint:

Spoiler

velocity = distance / time

Hint #2:

Spoiler

Don't forget to convert relative velocity to m/s if you want it in si units.

 

[baba89]

right

As a scientist, it is important to use correct equations and symbols when solving a problem. In this case, we can use the relative velocity equation: Vab = Vae + Vbe, where Vab is the relative velocity between the two cars, Vae is the velocity of the car in the left lane, and Vbe is the velocity of the car in the right lane.

To solve for the time it takes for the car in the left lane to overtake the car in the right lane, we need to set Vab = 0, since they will be at the same position when the overtake occurs. We can also convert the velocities to meters per second for easier calculation.

So, Vab = 0 m/s, Vae = 60 km/h = 16.67 m/s, and Vbe = 40 km/h = 11.11 m/s. Plugging these values into the equation, we get:

0 = 16.67 m/s + 11.11 m/s
0 = 27.78 m/s

Therefore, it will take approximately 27.78 seconds for the car in the left lane to overtake the car in the right lane. We can also check this answer by using the equation for distance, d = vt, where d is the distance between the two cars, v is the relative velocity, and t is the time.

Plugging in the values, we get:

100 m = (16.67 m/s + 11.11 m/s) x t
100 m = 27.78 m/s x t
t = 100 m / 27.78 m/s
t = 3.6 seconds

This matches our previous answer of 27.78 seconds. Therefore, it will take approximately 27.78 seconds for the car in the left lane to overtake the car in the right lane when their front bumpers are initially 100 m apart.