## Suppose a car can accelerate at 1m/s2. How large a break in traffic is needed to enter a highway where cars?

Suppose a car can accelerate at 1m/s2. How large a break in traffic is needed to enter a highway where cars are moving a 20m/s if the drive wants to avoid forcing the next car to slow down or to approach closer than 25m?

July 20th, 2010 at 6:25 pm

This question cannot be answered. It will be wrong to assume that car can decelerate at the same rate at which it can accelerate. If it is given that the car can decelerate at the rate of 1 m/s^2, then the question can be answered as under.

If s = distance covered after applying brakes,

v^2 = u^2 – 2as

=> s = u^2 / 2a = (20)^2 / 2 * 1 = 200 m

If a minimum of 25 m is to be kept, The break in traffic needed = 225 m

July 20th, 2010 at 6:32 pm

Assumptions:

1) The entering car is stopped

2) The entering car begins accelerating as soon as the rear bumper of the car it will fall in behind passes its front bumper.

What distance does it take a car to accelerate from 0 to 20 m/s at a rate of 1m/s²?

1) Final velocity = initial velocity + acceleration * time

2) Distance = initial velocity * time + 1/2 acceleration * time²

Plugging in the known values, the first equation becomes

20 m/s = 0 m/s + 1m/sec² * x

x = 20 sec

Now we can calcuate the second equation

D = 0 m/s * 20 sec + 1/2 * 1 m/s² * (20 sec)²

D = 0 m + 200 m

If we need to keep a 25 m space behind us, that gets added to the necessary distance.