Antiderivatives: Car Deceleration ProblemA car braked with a constant deceleration of 40 ft /...

Villaretq0

Villaretq0

Answered

2022-06-24

Antiderivatives: Car Deceleration Problem
A car braked with a constant deceleration of 40  ft / s 2 , producing skid marks measuring 160 ft before coming to a stop. How fast was the car travelling when the brakes were first applied?
I know I can solve this problem using kinematics equations from physics; using v f 2 = v i 2 + 2 a d yields an initial velocity of 113 ft/s. However, I am supposed to be using antiderivatives and not physics. So far, I figured that if a ( t ) = 40 then v ( t ) = 40 t + c 1 and d ( t ) = 20 t 2 + c 1 x + c 2 , where c 1 and c 2 are constants. I'm not quite sure what my next step should be... any suggestions?

Answer & Explanation

popman14ee

popman14ee

Expert

2022-06-25Added 19 answers

Explanation:
Your equations are correct ( with a t instead of x in the second equation) and, if we measure the time and the space from the instant in which began the braking, in your second equation we have c 2 = 0 ( the initial position is d ( 0 ) = 0). the other constant c 1 is the inital velocity v ( 0 ) = c 1 and at the instant t 1 in wich the car stops its motion we have:
{ 0 = 40 t 1 + v ( 0 ) 160 = 20 t 1 2 + v ( 0 ) t 1 solve this system and you find the duration of the braking t 1 and the inital velocity v(0).

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