Question

Determine the work done by a force

F

ˆ

i

ˆ

j k

ˆ

 xy  yz  xz



in taking a particle along

the path defined by the equation

( )

ˆ

2

ˆ ˆ

, 0 1

2 3

r t  t i  t j  t k t 



from

t  0

to

t  2.

Is the force conservative?​

Answer 1

Work is done whenever a force moves something over a distance. You can calculate the energy transferred, or work done, by multiplying the force by the distance moved in the direction of the force.

The particle travels along the path defined by the parabola y = 0.5x^2. If the component of velocity along the x axis is vx = (5t) ft/s, where t is in seconds, determine the particle’s distance from the origin O and the magnitude of its acceleration when t = 1 s. When t = 0, x = 0, y = 0.

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