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September 21, 2014

Homework Help: Calculus

Posted by Aletha on Sunday, March 18, 2007 at 6:51pm.

After t hours of an 8-hour trip the distance a car travels is modeled by:
D(t)= 10t + (5)/(1+t) - 5
where D(t) is measured in meters.

a) derive a formula for the velocity of the car.
b) how fast is the car moving at 6 hours?
c) derive a formula for the car's acceleration.

My answers:
a)(5)/(1-t)^2
b).6 meters (I KNOW this is wrong!)
c) (10t)/t(1-t)

I just know my answers are wrong if someone could just tell me where I went wrong?

Your derivative, (the velocity), should have been 10 -5(1+t)^2

now substitute t=6 into that.

your acceleration, the second derivative, should be

10/(1+t)^3

oops, forgot the divistion sign

first derivative is 10-5/(1+t)^2

for the velocity derivative; I get 5/49 which is .102 meters? That still doesn't sound right.
For the acceleration are you taking the 2nd derivative... because if so; why still have the 10?

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