## Antiderivatives

1. The problem statement, all variables and given/known data

A car going 70km/h comes to a stop in 6 seconds, assume that the deceleration is constant, find the distance traveled using a graph; find the distance traveled using antiderivatives.

3. The attempt at a solution

If the deceleration is constant, I would assume that the slope (derivative) of the graph would also be constant, hence the graph should look like a straight line with a negative slope.

Converting 70km/h into m/s, I get 19.4m/s. To calculate the distance, I simply took the area under the curve, which is a triangle:

(19.4 x 6)/2 = 58.2m

But when I'm using antiderivatives to solve this, I get a different answer...

S(6) = intergral v(t)dt = 19.4 (6) = 116.4m

It seems like this answer is twice as much as the one when calculated using a graph, and I'm sure the graph should be the right answer... could someone please tell me which part did I do wrong?

 PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age
 Recognitions: Homework Help Science Advisor The velocity is not constant, but rather a function of time.. $$\int kt dt = \frac{1}{2} k t^2+C$$
 Thanks for your correction Nate. I'm still a bit confused though, if velocity at time 0 = 19.4, and that at time 6 is 0, wouldn't C always equal to 0?

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