A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10. What is the position of the car when t = 20? You must show your work answer to 3 decimal places. Include units in your answer.

Question

I'm sure this problem isn't all that difficult, but I'm having a lot of trouble solving. Please help!

Answer 1

I cannot see the graph, but you have the graph for a(t)
v(t) = ∫ a(t) dt + C
But, since v(0) = 0, C=0
Now you know that the position
s(t) = ∫ v(t) dt + C
Since s(0) = 10, you can solve that for C.
Now just find s(20)

Answer 2

I'm still confused, how exactly am I supposed to plug this in?

Answer 3

sigh. what does the graph of the acceleration look like?
Is it constant? a step function? a sloping line?
piecewise? Give me the equation of the line(s) so I can know what to do.
Unless you give me something to go on, there's not much I can do.

review your section on antiderivatives. That will explain how to go from acceleration to velocity, and thence to position.

Answer 4

I apologize, but the website isn't letting me put in the graph. It has a -1 slope and is a decreasing linear graph. Everything else is given in the problem.