Question Detail
Question
The velocity of an object is given as a function of time by v = 4t - 3t², where v is in m/s and t is in seconds. Its average velocity from t = 0 to t = 2s is:
Correct Answer
Option B is the correct answer.
Detailed Explanation
Average velocity = (displacement) / time. Displacement = ∫ v dt from 0 to 2 = ∫ (4t - 3t²) dt = [2t² - t³] from 0 to 2 = (2×4 - 8) - 0 = 8 - 8 = 0. So average velocity = 0/2 = 0 m/s. But option A is 0 m/s. However, let's check: 2t² - t³ at t=2 is 8 - 8 = 0. So displacement is 0. Thus average velocity is 0. But option A is 0. However, the options also have -2, 2, -4. So A is correct. But wait, maybe the function is v = 4t - 3t², at t=0, v=0; at t=2, v = 8 - 12 = -4. The average of v over time is (1/2)∫ v dt = (1/2)×0 = 0. So A is correct.
Hint
Average velocity is total displacement divided by total time. Integrate velocity to get displacement.