The coordinates of an object moving in the xy plane vary with time according to the following equations x = −7.16 sin ùt and y = 4.00 − 7.16 cos ùt, where ù is a constant, x and y are in meters, and t is in seconds. Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time t 0. (Use the following variables as necessary: omega for ù and t.)

Question

The coordinates of an object moving in the xy plane vary with time according to the following equations x = −7.16 sin ùt and y = 4.00 − 7.16 cos ùt, where ù is a constant, x and y are in meters, and t is in seconds. Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time t > 0. (Use the following variables as necessary: omega for ù and t.)

For the position vector I got:
-7.16sin(omega*t)i+4.00-7.16cos(omega*t)j
For the velocity vector I got:
-7.16*omega*cos(omega*t)i+7.16*omega*sin(omega*t)j
For the acceleration vecotr I got:
7.16*omega^2*sin(omega*ti)+7.16*omega^2*sin(omega*t)j

I this correct or not? My homework is computer based and when I type this in, it marks it wrong. Please help.

bobpursley · Answer

The only two things I see wrong is you have on acceleration the unit vector i inside the argument of the sin function, and on the lst part of the acceleration vector, you should have COSINE, not sine

Damon · Answer

One error
For the acceleration vector I got:
7.16*omega^2*sin(omega*ti)+7.16*omega^2*__________sin(omega*t)______j

should be

For the acceleration vector I got:
7.16*omega^2*sin(omega*ti)+7.16*omega^2*cos(omega*t)j

Note that
acceleration = - omega^2 *( sin and cos components of displacement)