# help needed changing words to formula for integration

• Sep 10th 2010, 04:41 PM
help needed changing words to formula for integration
Hey guys,

I know how to get the answer but I don't know what the formulas are (Worried)

The questions goes..

You start at rest on a bike. You accelerate at 1 m/s^2 for 4 seconds and then travel at a constant velocity until you arrive at your destination which is 80 metres from the starting position. Calculate travelling time.

I know I have to integrate twice to find the distance traveled during the acceleration period but I don't know what the formula for this question will be. I have a(t) = t ? But I don't get the correct answer when I integrate..

I can do the question in my head easy but we have to use integration.

Thanks
• Sep 10th 2010, 10:08 PM
sa-ri-ga-ma
Why can't you use the kinematic equations to solve this problem? Is there any instruction to solve this problem by integration?
• Sep 11th 2010, 04:20 AM
tom@ballooncalculus
Just in case a picture helps, and if you do want or need to derive the formulae by integration from the definitions of velocity v and acceleration a in terms of displacement, s ...

http://www.ballooncalculus.org/asy/second/motiona.png

... where straight lines are differentiating downwards with respect to t. Well, integrating a twice with respect to t ...

http://www.ballooncalculus.org/asy/second/motionb.png

Spoiler:
http://www.ballooncalculus.org/asy/second/motion.png

Spoiler:
http://www.ballooncalculus.org/asy/second/motion6.png

So after 4 seconds the displacement is 8, and you've 72 metres to go, at 4 m/s.

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!
• Sep 12th 2010, 03:06 AM
Its for a calculus course I am doing so I just assumed they would want me to use calculus to find the answer.
• Sep 12th 2010, 03:44 AM
mr fantastic
Quote:

Hey guys,

I know how to get the answer but I don't know what the formulas are (Worried)

The questions goes..

You start at rest on a bike. You accelerate at 1 m/s^2 for 4 seconds and then travel at a constant velocity until you arrive at your destination which is 80 metres from the starting position. Calculate travelling time.

I know I have to integrate twice to find the distance traveled during the acceleration period but I don't know what the formula for this question will be. I have a(t) = t ? But I don't get the correct answer when I integrate..

I can do the question in my head easy but we have to use integration.

Thanks

I suggest that you start by drawing a velocity-time graph.
• Sep 12th 2010, 05:43 AM
HallsofIvy
No, a(t) is not t. You are told that the acceleration is 1 m/s^2 for 4 seconds- a(t)= 1. What is the velocity function at each time t for those 4 seconds? What will your velocity be at the end of the 4 seconds? What will your position be at the end of the 4 seconds? What distance do you still have to go to get to a total of 80 m? How long will that take at your new velocity?
• Sep 12th 2010, 03:48 PM