Your speed from the time you hit the brakes is
v(t) = 18-10t
so, it takes you 1.8 seconds to stop
your distance from the time you hit the brakes is
s(t) = 18(t+0.5)-5t^2
so, s(1.8) = 18*2.3 - 5*1.8^2 = 25.2m
so, 17m looks like a good answer.
You want the maximum speed v such that s(t) < 42
you have speed = v-10t, so time to stop is v/10 seconds.
So, figure v such that s(t)=42 and anything less than that will stop before hitting the deer.
v(v/10+0.5) - 5(v/10)^2 = 42
v = 24.41 m/s
You're driving down the highway late one night at 18 m/s when a deer steps onto the road 42 m in front of you. Your reaction time before stepping on the brakes is 0.50 s , and the maximum deceleration of your car is 10 m/s2 .
A.)How much distance is between you and the deer when you come to a stop?
I got 17m.
B.)What is the maximum speed you could have and still not hit the deer?
I really don't know how to get Vmax.
Someone please help me. Thank You!
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