# Homework Help: How long will it take to overtake

1. Mar 10, 2012

### joseph0205

there a two cars, the one behind is travelling at 100km/hr, the one in front is traveling at 95 km/hr. say the car lengths are 4.73 metres and between the two cars is 55.57 metres. no acceleration for either cars.

will the car at the back be able to over take the other car within 2.1km?

could you also please show the equation you used, its for a physic assignment due monday thanks :)

2. Mar 11, 2012

### PeterO

I will explain with simpler numbers - you can repeat with the real values.

Make the cars 5m long, and the gap between them 50m

I am assuming that at first, the front of the fast car is 50m from the back of the slow car.
After overtaking, then moving back to his lane when the gap is again 50m, we now have the front of the fast car 60m in front of the slow car [so that the rear of the fast car is 50m in front of the slow car.
That means the fast car has to gain 110m

Convert those speeds to m/s and you get something like 25m/s and 30m/s [you can use the real numbers remember]
That means the fast car is gaining 5m each second.
To move up the 110 m that would take 22 seconds.

At 30m/s, the fast car will cover 660m in that time.

I chose easy numbers to use for explanation purposes. You need to use the real numbers in a similar way to see how far the cars travel during this manoeuvre.