Find the power of a force

F= (10 N)ˆý +(−4 N)ˆj if the velocity v = (−4 m/s)ˆý +(4 m/s)ˆj.
Answer in units of W
(^i and ^j means i hat and j hat)

F dot v = -40 -16 = -56 Watts

To find the power of a force, we can use the formula:

Power (P) = Force (F) dot Product Velocity (v)

First, we need to calculate the dot product of the force and velocity vectors.

The dot product of two vectors is calculated by multiplying their corresponding components and summing them together.

Now let's calculate the dot product of the given force and velocity vectors.

Force (F) = (10 N)ˆý +(−4 N)ˆj
Velocity (v) = (−4 m/s)ˆý +(4 m/s)ˆj

Calculating the dot product:

(F dot v) = (10 N) * (−4 m/s) + (−4 N) * (4 m/s)
= (-40 N * m/s) + (-16 N * m/s)
= -56 N * m/s

The unit of the dot product is N * m/s.

Finally, we have calculated the power of the force. The power is equal to the dot product of the force and velocity vectors.

Thus, the power (P) = -56 N * m/s (unit of power is Watt, W).