A ranger in a national park is driving at 15.0 m/s when a deer jumps into the road 60 m ahead of the vehicle. After a reaction time, t, the ranger applies the brakes to produce an acceleration of a = -3.00 m/s2. What is the maximum reaction time allowed if she is to avoid hitting the deer?
Question
Answer:
t = 5 s
Explanation:
In uniform rectilinear movement, the equation for final speed is:
vf = v₀ + a*t
In this case we need that the car stops just before 60 m after applied the brakes, then
vf = v₀ – a*t
vf = final speed = 0
v₀ = initial speed = 15 m/s
And negative acceleration is 3 m/s²
0 = 15 (m/s) – 3 ( m/s²)*t
t = 15 / 3 (m/s /m/s²)
t = 5 s
The point is that with that value ranger will hit the deer so in order to not to hit the deer that time should be smaller than 5 seconds