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

Answer:

18.21 m

41.1 m

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

Part A

$v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-17.9^2}{2\times -8.8}\\\Rightarrow s=18.21\ m$

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

Part B

$v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-17.9^2}{2\times -3.9}\\\Rightarrow s=41.1\ m$

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