Suppose that an object is attached to a spring and is startebd in motion ?

Suppose that an object is attached to a spring and is started in motion so that the speed at time t is given [5cos(t)]. How far did the object travel from t=0 to t = 2pi? (Use the Fundamental Theorem of Calculus)Suppose that an object is attached to a spring and is startebd in motion ?Distance Traveled, d = ut + 1/2 a t^2 --------- 1

Where u = initial velocity

t= time

a= acceleration



Now we know that rate of change of velocity is acceleration,



Then a= dv/dt = d (5 Cos t)/dt = -5 sin (t)

And u at t= 0 is u = 5



Then Equation 1 Became

d = 5t-1/2 (5 sin (t) t^2

Then At t = 2 Pi

d= 5*2*Pi - 20 Pi^2 Sin (2Pi)

Then d = 10 Pi = 10蟺