Question

what is the difference between instantaneous velocity and average velocity?
a) average velocity happens in a particular instant, instantaneous velocity is the velocity of an object over a longer period of time.
b) instantaneous velocity is never right, average velocity is always right
c) instantaneous velocity happens in a particular instant, average velocity is the velocity of an object over a longer period of time.
d) none of the above

question 7 (1 point)
if you were to find the area under a velocity - time graph, which of the following quantities would you be calculating?
(a) displacement (b) instantaneous velocity
(c) average acceleration (d) time

Explanation:

• For the first question:
• Instantaneous velocity is the velocity of an object at a particular instant.
• Average velocity is the total displacement divided by the total time taken (i.e., the velocity of an object over a longer period of time).
• Option a has the definitions reversed.
• Option b is incorrect as both instantaneous and average velocity can be correct depending on the context.
• Option c has the correct definitions.
• For the second question:
• The area under a velocity - time graph is calculated as \(A=\int_{t_1}^{t_2}v(t)dt\).
• By the fundamental theorem of calculus, if \(v(t)=\frac{ds}{dt}\) (where \(s\) is displacement), then \(\int_{t_1}^{t_2}v(t)dt=s(t_2)-s(t_1)\), which is displacement.
• Instantaneous velocity is the slope of the displacement - time graph.
• Average acceleration is \(\frac{\Delta v}{\Delta t}\) (the slope of the velocity - time graph).
• Time is just the independent variable on the x - axis of the velocity - time graph.

Answer:

• First question: C. Instantaneous velocity happens in a particular instant, Average velocity is the velocity of an object over a longer period of time.
• Second question: A. displacement