You're driving down the highway late one night at 20 m/s when a deer steps onto the road 41m in front of you. Your reaction time before stepping on the brakes is 0.50s, and the maximum deceleration of your car is 10 m/s2. What is the maximum speed you could have and still not hit the deer?

Maximum speed you could have and still not hit the deer = 24.07 m/s

Explanation:

Let the maximum speed you could have and still not hit the deer be y.

Your reaction time before stepping on the brakes is 0.50s.

Distance traveled during this time = 0.5y

A deer steps onto the road 41m in front of you

Remaining distance to deer = 41 - 0.5y

The maximum deceleration of your car is 10 m/s²

We have equation of motion, v² = u² + 2as

Initial velocity, u = y m/s

Final velocity, v = 0 m/s

Acceleration, a = - 10 m/s²

Displacement, s = 41 - 0.5y

Substituting,

v² = u² + 2as

0² = y² + 2 x - 10 x (41 - 0.5y)

20 (41 - 0.5y) = y²

820 - 10 y = y²

y² + 10 y - 820 = 0

y = 24.07 m/s or y = - 34.06 m/s (not possible)

Maximum speed you could have and still not hit the deer = 24.07 m/s