Question

A car is going south on I-69 at 33 m/s (74 mph). The car has good brakes so its maximum braking acceleration is – 8.5 m/s^2 . Traffic has come to a stop in all lanes 120 m ahead. What is the maximum reaction time the driver can have and still be able to stop in the available distance? Hint: During the driver’s reaction time, the car continues to have the initial velocity of 33 m/s.

Answer 1

1.69515 seconds

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=(0^2-33^2)/(2* -8.5)\\\Rightarrow s=64.06\ m`

The distance between the traffic and the car after braking is 120-64.06 = 55.94 m

Time = Distance / Speed

`\text{Time}=(55.94)/(33)\\\Rightarrow \text{Time}=1.69515\ seconds`

The reaction time cannot be more than 1.69515 seconds