anonymous
  • anonymous
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 velocity of the car when t = 6? You must show your work and include units in your answer.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
https://gyazo.com/ca4a1cefd3d5cea67189b222a3ad438d
SolomonZelman
  • SolomonZelman
Can you find the acceleration function for me please?
SolomonZelman
  • SolomonZelman
(All I want is: "What line is graphed on the curve?" )

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SolomonZelman
  • SolomonZelman
I noticed that (10,0) and (0,10) are points on the acceleration function. So what is the equation of your acceleration function?
SolomonZelman
  • SolomonZelman
a(t)=?
anonymous
  • anonymous
Would it not be y=-x+10?
SolomonZelman
  • SolomonZelman
yes exactly
SolomonZelman
  • SolomonZelman
a(t)=-x+10
SolomonZelman
  • SolomonZelman
the acceleration is the slope/derivative of the velocity.
SolomonZelman
  • SolomonZelman
So what do you have to do to the a(t) to find the velocity function v(t)?
anonymous
  • anonymous
Integrate.
SolomonZelman
  • SolomonZelman
Yes, and what do you get when you integrate -x+10 ?
anonymous
  • anonymous
-x^2/2 + 10x
SolomonZelman
  • SolomonZelman
Yes +C
SolomonZelman
  • SolomonZelman
but, in our case we know that t=0, velocity is 0. So, (0,0) is a point on the function v(t), and you can use that fact to solve for C, which will yield C=0.
SolomonZelman
  • SolomonZelman
v(t) = -x²/2 +10x and you need v(6).... good luck!
anonymous
  • anonymous
42?
SolomonZelman
  • SolomonZelman
-36/2 + 60 -18 + 60 42 YES
anonymous
  • anonymous
Thank you good sir

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