Question

this is a physics question that requires a lot of math. Hoping on of you genius could help me.

Q: You're driving down the highway late one night at 16m/s when a deer steps onto the road 44m in front of you. Your reaction time before stepping on the brakes is 0.50s , and the maximum deceleration of your car is 10m/s2 .

How much distance is between you and the deer. I solved this =23m

What is the maximum speed you could have and still not hit the deer?

The answer is 25 m/s. A lot of people had stated to use the quadratic formula. I just don't know where to begin.

Answer 1

Have you considered hitting it one piece at a time?

Reaction Distance: Speed * 0.50 s
Initial Problem: 16 m/s * 0.50 s = 8 m

Braking Acceleration: a(t) = -10 m/s^2 -- This is constant.
Braking Velocity: s(t) = -10 m/s^2 (t) + "Initial Velocity"
Initial Problem: s(t) = -10 m/s^2 (t) + 16 m/s
Braking Location: x(t) = -5 m/s^2 (t^2) + 16 m/s (t) - "Initial Location"
Initial Problem: x(t) = -5 m/s^2 (t^2) + 16 m/s (t) - (44 m - 8 m)

Having said all that, the first question makes no sense. Does it mean the distance when the vehicle stops?

s(t) = -10 m/s^2 (t) + 16 m/s = 0 ==> t = 16/10 s = 8/5 s
That's how long it takes to stop. Where are we when that happens?
x(8/5) = -5 m/s^2 ((8/5 s)^2) + 16 m/s (8/5 s) - (44 m - 8 m) = -23.2 m
This seems to be a little different from your response.

Now, the challenge is to do this all over again, but missing the initial velocity.

Initial Velocity: V -- Let's just call it this so we can talk about it.
Initial Distance is the same: 44 m -- No change.
Reaction Distance: V/2
Braking Acceleration: a(t) = -10 m/s^2 -- No Change
Braking Velocity: s(t) = -10 m/s^2 (t) + V -- Missing V!
Braking Location: x(t) = -5 m/s^2 (t^2) + V (t) - (44 m - V/2 m)

When do we stop? s(t) = -10 m/s^2 (t) + V = 0 ==> t = V/10 s
Where do we stop? x(t) = -5 m/s^2 ((V/10 s)^2) + V (V/10 s) - (44 m - V/2 m) = 0 -- We might just brush the poor, frightened deer.

One piece at a time! Slowly. Methodically.

Answer 2

BTW: I get 25.083 m/s