the power of an engine is the derivative of the work that it performs with respect to time. suppose an engine outputs work modeled by the function w(t)=x^2-3 where W is power in joules and t is time in seconds. which equation represents its power at a given time t?
The power at a given time t is the derivative of the work function w(t) with respect to time t:
P(t) = w'(t)
Since w(t) = x^2 - 3, we have:
w'(t) = 2x*dx/dt = 2x
To find x in terms of t, we need to solve for x in the equation w(t) = x^2 - 3:
x^2 - 3 = w(t)
x^2 = w(t) + 3
x = ±sqrt(w(t) + 3)
However, since we want the power P(t) = 2x, we only need the positive square root:
x = sqrt(w(t) + 3)
Therefore, the equation for the power at a given time t is:
P(t) = 2x = 2sqrt(w(t) + 3)
or
P(t) = 2√(t^2 - 3)