chp 4, \"Physics for scientists and engineers\" Eighth edition #4 The coordinate
ID: 2005612 • Letter: C
Question
chp 4, "Physics for scientists and engineers" Eighth edition
#4
The coordinates of an object moving in the xy plane vary with time according to the equation
x=-5.00 sin t , y=4.00-5.00 cos t, where is a constant
x and y in meter, t in s
(a) Determine the components of velocity of the object at t=0
(b) Determine the components of acceleration of the object at t=0
(c) Write expressions for the position vector, , the velocity vector, and the acceleration vector of the object at any time ( t larger than 0)
(d) describe the path of the object in an xy plot.
Explanation / Answer
The coordinates of an object moving in the xy plane vary with time according to the equation
x=-5.00 sin t , y=4.00-5.00 cos t, where is a constant
x and y in meter, t in s
(a) Determine the components of velocity of the object at t=0
velocity=dx/dt
so Vx=[dx/dt] = -5cost
at t=0 Vx=-5w
similarly Vy=[dy/dt] =0+5sint=0
(b) Determine the components of acceleration of the object at t=0
acceleration=dv/dt
so ax=+52sint
at t=0 ax=0
ay=-52cost
at t=0 ay=-52
(c) Write expressions for the position vector, , the velocity vector, and the acceleration vector of the object at any time ( t larger than 0)
position vector for displacement =-5.00 sin ti +(4.00-5.00 cos t)j
position vector for velocity -5costi+5sint
position vector for acceleration= 52sinti+-52costj
(d) describe the path of the object in an xy plot.
its path will be like a transverse wave
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