Calculus

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?

  1. 👍 0
  2. 👎 0
  3. 👁 157
asked by Aletha

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

    asked by Aletha on March 18, 2007
  2. Calculus

    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)

    asked by Aletha on March 18, 2007
  3. physical science

    A car travels in a northward direction for a total distance of 512 km. The car completes this trip in 6 hrs. After resting the driver makes the return trip, the return trip only takes 5.5 hours. What is the average speed of the

    asked by Anonymous on August 21, 2014
  4. Math

    The table shows the number of miles driven over time. Time (hours)----------Distance (miles) 4---------------------232 6---------------------348 8---------------------464 10--------------------580 Express the relationship between

    asked by Kaai97 on December 16, 2015
  5. Algebra

    A bird leaves his nest and travels 20 miles per hour downward for x hours. On the return trip the bird travels 4 miles per hour slower and has six miles left after x hours. What is the distance of the entire trip? How long does

    asked by teresa on September 8, 2016
  6. Math

    A bird leaves his nest and travels 20 miles per hour downward for x hours. On the return trip the bird travels 4 miles per hour slower and has six miles left after x hours. What is the distance of the entire trip? How long does

    asked by Teresa on September 8, 2016
  7. Algebra 1

    The table shows the number of miles driven over time. Time|Distance 4 |184 6 |276 8 |368 10 |460 Express the relationship between distance and time in simplified form as a unit rate. Determine which statement correctly interprets

    asked by basketball&batman on December 1, 2015
  8. Calculus

    The velocity of a car (in miles per hour) is given by v(t) = 61.25t − 17.5 t^2 where t is in hours. Write a definite integral for the distance the car travels during the first 2.5 hours. Use your graphing calculator to find this

    asked by Jane on November 14, 2010
  9. math

    the el paso middle school girls baxketball team is going from el paso to san antonio for the texas state championship game.the trip will be 560 miles.their bus travels at an average speed of 60 miles per hour. estimate the

    asked by chemiii on October 2, 2006
  10. algebra

    A car travels down the highway at speeds between 50 miles per hour and 65 miles per hour. If the car travels for 4 hours, write an expression that represents the distance, d, the car has travelled.

    asked by lala on November 1, 2013

More Similar Questions