Question

At the instant that the velocity of the crate is v⃗ =(3.40m/s)ι^+(2.20m/s)j^, what is the instantaneous power supplied by this force?

Answer 1

I found some missing information about this problem online. We are given the force:
$F = F =(-7.50N)i +(3.00N)j$
Power is defined as the rate of doing work. 
This is the formula:
$P= \frac{dW}{dt}$
Where P is power, W is work. 
Work is defined as:
$W=F\cdot r$
F is the force and r is the displacement.
If we assume that force is not changing (it's constant) with time we get:
$P= \frac{dW}{dt}=F \frac{dr}{dt}=F\cdot v$
Keep in mind that both force and velocity are vectors, so we have to multiply each component separately.
Finally, we get:
$P=F_i\cdot v_i+F_j\cdot v_j=(-7.50N)(3.40\frac{m}{s})+(3.00N)(2.20\frac{m}{s})= -18.9 W$