Need help with last question - asking what is final velocity Course Contents....

Question

Need help with last question - asking what is final velocity Course Contents....Differential Equations and Integrals Acceleration Graph ol a Car Graphs and Integrals 2. 5 1.75 1.5 1.23 it is 8.75 0.5 0.25 In other words: Acceleration is the time derivative of velocity .25 0,5 -0.75 At t0, a car drives with a velocity of r(t 0)m/s. Its acceleration on a straight road is shown over the next minute. Which one of the following statements is true? Incorrect The car first starts driving backwards and then forwards Correct: The car first speeds up and then slows down. Incorrect The car first drives forwards and then backwards, Incorrect The car first slows down, then speeds up, and then slows down again. Incorrect None of the above 1.25 1.5 1.75 2.25 2.5 0 S 10 15 20 25 30 35 4 45 50 55 60 Tise (s) Previous Tries r receipt no. is 152-6725 At what time does it have maximum velocity? 25.7s What is the maxinum velocity? 17m/s ou are correct recelpt no, is 152-8316 Previos.Tr What is the final velocity? 00 ms Tries 2/12 Previous Tries

Explanation / Answer

Looking at the symmetry of the curve, if we consider the areas enclosed by both the bumps, they give us equal value but of opposite sign( since for first bump acceleration is positive but for the next bump it is negative). Sum of both results in zero. But area under the curve is nothing but the value of the integral. i.e. the second term in r.h..s of velocity equation vanishes and we end up with v(t)=v0=5m/s.

so final velocity will be 5m/s.

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