Question

A student is driving to school on a road with a speed limit of 40mph (17.9 m/s). A stoplight ahead of her turns yellow, so she begins to slow down to come to a stop. On a dry day, she is able to make her car slow down with an acceleration of magnitude of 8.8 m/s^2. However, if the road is wet, she can only manage an acceleration with a magnitude 3.9 m/s^2. Part A:

On a dry day, how far (in meters) from the intersection would the student need to start braking in order to stop in time?
Part B:
If it were raining instead, how far (in meters) from the intersection would the student need to start braking?

Answer 1

18.21 m

41.1 m

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

Part A

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=(0^2-17.9^2)/(2* -8.8)\\\Rightarrow s=18.21\ m`

On a dry day she would have to start braking 18.21 m away from the intersection

Part B

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=(0^2-17.9^2)/(2* -3.9)\\\Rightarrow s=41.1\ m`

On a wet day she would have to start braking 41.1 m away from the intersection