(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A sportscar, Fiasco I, can accelerate uniformly to 68 m/s in 30 s. Its maximum braking rate cannot exceed 0.75g. What is the minimum time required to go 1300 m, assuming the car begins and ends at rest?

(Hint: A graph of velocity vs. time can be helpful.)

2. Relevant equations

No "equations" really, rather, just the calculus relationship between position, velocity, and acceleration.

3. The attempt at a solution

In constructing a velocity vs. time graph, I found the acceleration (or slope of the line) to be 68m/s / 30 s = 2.27m/s^{2}. Likewise, the acceleration (or slope) when the car is decelerating is .75*9.81m/s^{2}=-7.36m/s^{s}.

Obviously, the area under the curve of this graph is the distance travelled by the car. I calculated that in order for the car to travel 1300m at its constant acceleration of 2.27m/s^{2}, it would need to travel for 33.9 seconds. [The integral from 0 to 33.9 of 2.27t = 33.9].

This above calculation is probably irrelevant to the problem at hand, but I have NO CLUE as to where the car should stop accelerating and put on its brakes. Is this a differential equation problem possibly? Somehow I need to figure out the maximum time the car can accelerate in order for it to slam on its brakes and skip to a stop so that its total distance traveled is exactly 1300m. What calculus is used to find this mid-point of acceleration to deceleration?

Any help would be greatly appreciated! Thanks!

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# Homework Help: Velocity vs. Time with Uniform Acceleration and Braking Rate

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