Answer:
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
