IB Physics Average power or power?

A tutorial sheet of questions on power is given below.

  1. Define instantaneous power.
  2. Define average power.
  3. Is average power always one-half the maximum power ?
  4. Which is the correct equation, 𝘗 = Fv or 𝘗 = Fv cos𝜃 ?
  5. The resultant force acting on an object is given by F = a v + b, where v is the speed of the object and a and b are constants. The "area" under the graph of F versus v between v = 0 and v = V is equal to (a) the power when v = V, (b) the average power from v = 0 to v = V, (c) the total power from v = 0 to v = V (d) none of the above
  6. The engine of a car of mass m has a constant power output P. A drag force kv acts on the car as it is driven along a horizontal road, where v is the speed of the car. If the car starts from rest the speed of the car (a) increases at a constant rate, (b) increases at an increasing rate, (c) increases at a decreasing rate, (d) remains zero due to drag force.
  7. In question 6 the speed of the car (a) approaches a maximum value, (b) reaches a maximum value, (c) continues to increase, (d) approaches a maximum value that is proportional to k.