Question

You drive on Lincoln Way in a BMW M3 at a speed of 30.0 mi/hr and approach the intersection at University Drive. The maximum deceleration of the M3 is 9.80 m/s2 . a. How many meters from the intersection do you need to start braking the latest in order to come to a stop at a red light? b. How much time passes before your car comes to a halt?

Answer 1

9.17649955924 m

1.36848639456 seconds

Step-by-step explanation:

t = Time taken

u = Initial velocity = 30 mi/h

v = Final velocity = 0

s = Displacement

a = Acceleration = -9.8 m/s² (-ve due to deceleration)

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=(0^2-((30* 1609.34)/(3600))^2)/(2* -9.8)\\\Rightarrow s=9.17649955924\ m`

The distance before reaching the intersection must be at most 9.17649955924 m not less than that.

`v=u+at\\\Rightarrow t=(v-u)/(a)\\\Rightarrow t=(0-(30* 1609.34)/(3600))/(-9.8)\\\Rightarrow t=1.36848639456\ s`

The time to come to a halt is 1.36848639456 seconds