An example of a word problem that requires the use of integration is: a particle moves with a velocity given by v = 3t^2 + 4t + 16. What is the distance traveled by the particle in the first 5 seconds.
The result is: `int_(0)^5 3t^2 + 4t + 16 dt`
`int_(0)^5 3t^2 + 4t + 16 dt`
=> `3t^3/3 + 4t^2/2 + 16t` between t = 0 and t = 5
=> `5^3 - 0^3 + 2*5^2 - 2*0^2 + 16*5 - 16*0`
=> 125 - 0 + 50 - 0 + 80
My idea was to do something like
The velocity of a moving object can be described as
where t is in seconds and v is meters per second.. If the object starts at v=0 when t=0, how far has it traveled after 30 seconds?
Or something like that.
I just don't know how I should incorporate it into a theme