The coordinates of an object moving in the xy-plane vary with time according to the equations x = −9.14 sin ωt and y = 4.00 − 9.14 cos ωt, where ω is a constant, x and y are in meters, and t is in seconds.
(a) Determine the components of the velocity of the object at t = 0.
(b) Determine the components of the acceleration of the object at t = 0.

ni

(A) Vx = -9.14ωCosωt,

Vy = 9.14ωSinωt

(B) ax =9.14ω²Sinωt,

ay = 9.14ω²Cosωt

Explanation:

The velocity of a body ia the time derivative of the poaition function of the body with respect to time. Given equations x = −9.14 sin ωt and y = 4.00 − 9.14 cos ωt,

All we need to do to get the velocity is to differentiate each of the equation above with respect to time in order to get Vx and Vy required of us.

Vx = dx/dt = -9.14ωCosωt and

Vy = dy/dt = 9.14ωSinωt

In order to get the acceleration we differentiate the velocity function with respect to time. That is,

A = dv/dt

ax = dVx/dt = 9.14ω²Sinωt

ay = dVx/dt = 9.14ω²Cosωt

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