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Kinematics motion -- Given position, find velocity and acceleration
A particle's position as a function of time is given by xf = xi . sin wt, where xi and w are constants.
a) Find expressions for velocity and acceleration.
b) What are the maximum values of velocity and acceleration.
xf = xi. sin(wt)
a) xf = xi. sin(wt)
velocity v = xf' = d/dt xi sin(wt) + xi d/dt sin(w.t) . d/dt w.t
xf' = xi cos(wt).w = xi.w.cos(wt)
acceleration = v' or xf " = [d/dtxi.w + xi d/dt w]cos(w.t) + xi.w d/dt (cos(w.t) . d/dt (w.t)
xf " = x dw/dt cos (wt) - xw^2 sin(w.t)
Can someone verify the above steps for me before I proceed to part (b)?
Homework Statement
A particle's position as a function of time is given by xf = xi . sin wt, where xi and w are constants.
a) Find expressions for velocity and acceleration.
b) What are the maximum values of velocity and acceleration.
Homework Equations
xf = xi. sin(wt)
The Attempt at a Solution
a) xf = xi. sin(wt)
velocity v = xf' = d/dt xi sin(wt) + xi d/dt sin(w.t) . d/dt w.t
xf' = xi cos(wt).w = xi.w.cos(wt)
acceleration = v' or xf " = [d/dtxi.w + xi d/dt w]cos(w.t) + xi.w d/dt (cos(w.t) . d/dt (w.t)
xf " = x dw/dt cos (wt) - xw^2 sin(w.t)
Can someone verify the above steps for me before I proceed to part (b)?
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