Given y=xsin(x), 0≤t≤2π seconds, find the particle's displacement for the given time interval. If s(0)=4, where is it's final position?
First set up the integral with the bounds 0 to 2π as given. You are finding the integral, or antiderivative of 4cos(t) because the is the velocity function, and velocity is a first derivative function, so you want to find the value of the first derivative from 0 to 2π to find the displacement of the particle. Then use NINT once you set up the integral to solve it and find the displacement. As shown, this equals -6.285. Then you need to find the final position. You are already given that s(0)=4, so you just need to add the displacement to 4 to find the final position of -2.283.
Here's another example!
Given v(t)=.25t^3-t, 0≤t≤3 seconds, find the particle's displacement for the given time interval. If s(0)=4, where is it's final position?
Here's another example!
Given v(t)=.25t^3-t, 0≤t≤3 seconds, find the particle's displacement for the given time interval. If s(0)=4, where is it's final position?
Solve this problem to find the displacement in exactly the same way to get a displacement of .5625. Then, again, just add this number to 4 to get the final displacement.