Question

In designing a freeway on-ramp, you must make it long enough for cars to be able to accelerate and merge safely with traffic traveling at speeds of 75 mph . For an off-ramp, the cars must be able to come to a stop from 35 mph over the length of the ramp. Your traffic engineers provide the following data: Powerful cars can accelerate from rest to 50 mph in 4.0 s , while less powerful cars take twice as long to do this. When slowing down from 35 mph , a car with good tire treads will take 8.7 s to stop, whereas one with bald tires takes 15.2 s .

Answer 1

Displacement is inversely proportional to acceleration.

   Let us consider the vehicle with less power and acceleration

   Initial velocity of the car is,

v_o =0

   Initial time is,

t = 4 s

            v = 50 mph

            =22.35 m / s

   The acceleration of the car is

            a = (v - v_o) / t

                = 5.59 m /s²

  

So, braking distance or the length of the ramp required x is given by

            x = v t + (1 / 2) a t²

               = 134.1 m

   Initial time is,

t =8.7 s

            v = 35 mph

            =15.65 m / s

   The acceleration of the car is

            a = (v - v_o) / t

                = 1.80 m /s²

So, braking distance or the length of the ramp required x is given by

            x = v t + (1 / 2) a t²

               = 204.22 m