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.

Question

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.

anonymous · Answer

https://gyazo.com/ca4a1cefd3d5cea67189b222a3ad438d

solomonzelman · Answer

Can you find the acceleration function for me please?

solomonzelman · Answer

(All I want is:  "What line is graphed on the curve?" )

solomonzelman · Answer

I noticed that (10,0) and (0,10) are points on the acceleration function.
So what is the equation of your acceleration function?

solomonzelman · Answer

a(t)=?

anonymous · Answer

Would it not be y=-x+10?

solomonzelman · Answer

yes exactly

solomonzelman · Answer

a(t)=-x+10

solomonzelman · Answer

the acceleration is the  slope/derivative  of the velocity.

solomonzelman · Answer

So what do you have to do to the a(t) to find the velocity function v(t)?

anonymous · Answer

Integrate.

solomonzelman · Answer

Yes, and what do you get when you integrate -x+10 ?

anonymous · Answer

-x^2/2 + 10x

solomonzelman · Answer

Yes +C

solomonzelman · Answer

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 · Answer

v(t) = -x²/2  +10x

and you need v(6)....
good luck!

anonymous · Answer

42?

solomonzelman · Answer

-36/2  +  60
-18   +   60
42

YES

anonymous · Answer

Thank you good sir