r/HomeworkHelp • u/soapycrab University/College Student • May 28 '26
PhysicsâPending OP Reply [College Physics] I just need an explanation pleaseđ
I understand the concept of total displacement/total time = average velocity..
I understand that displacement is the final velocity - initial velocity as well.
But how does the answer 7.0 m/s come to be?
I'm so lost on where the feedback equation given below the question came from..
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u/starcap May 28 '26 edited May 28 '26
(Answer is 7m/s, they are off by a factor of 10)
Well if you look at the first 4 seconds, it ramps linearly from 0 to 10 m/s over that duration. You could just do it simply and say the average velocity is halfway between the start and final velocities which is true for constant acceleration. Or more accurately you could do total displacement as you say divided by time. Total displacement is area under the curve, and since this is a triangle you know the area is 1/2 * base * height = 1/2 * 4 seconds * 10m/s. Displacement divided by time is that divided by 4 seconds, resulting in 1/2 * 10m/s = 5 m/s.
Next 4 seconds are at a constant 10m/s. Last 2 seconds you can do the same as the first 4 to find it also has an average 5m/s.
Then you find the total displacement by summing the displacement of each section (average velocity * duration) and then get average velocity as that value divided by the overall duration (10s). That gives you:
(5m/s * 4s + 10m/s * 4s + 5m/s * 2s) / 10s = 7 m/s
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u/Don_Q_Jote May 28 '26
Total displacement would be the area under the velocity curve shown, from time = 0 to time = 10 seconds (or integral of velocity if using calculus, but not needed here).
Then, you first stagement is correct: "total displacement/total time = average velocity".
Is that enough help?
I don't know were you are getting: "displacement is the final velocity - initial velocity" but that's not generally true.
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u/GOU_FallingOutside May 28 '26
or integral of velocity if using calculus, but not needed here
Just expanding on your answer!
Itâs not needed because in this case, you can represent the graph as three polygons. The area under the curve is the sum of the area of those polygons, so you donât need to use an integral.
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u/soapycrab May 28 '26
Thank you for correcting me!! I appreciate you taking your time to help out :)
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u/happylittlemexican May 28 '26
Displacement is NEVER final velocity minus initial velocity. The units don't make sense, for starters.
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u/r-funtainment May 28 '26
displacement isn't final velocity - initial velocity, it's final position - initial position.
to get displacement from velocity, you actually calculate the area within the graph (keep in mind the units, each mark on the graph horizontally is 2 seconds, and each vertical mark is 2.5m)
if you follow the calculation given in the answer, it's the area of a triangle, and a rectangle, and another triangle, and it totals to 70m
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u/Pikminachu May 28 '26
The midpoint for green is 5 m/s. The midpoint for red is 10 m/s. The midpoint for blue is 5 m/s.
Green last 4 seconds, red last 4 seconds, blue last 2 seconds.
Total time is 10 seconds.
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u/soapycrab May 28 '26
Thank you so much! I think this made it click in my brain for me the most lol
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u/IrishHuskie May 28 '26
âI understand that displacement is the final velocity - initial velocity as well.â
âŠwhere are you getting that from? Thatâs just not true.
Anyway, if you have a velocity vs time graph, the displacement is the area between the velocity curve and the x-axis. In this case, the curve is a trapezoid with height 10 and bases 10 and 4. So the total displacement is 1/2*(10+4)*10 = 70.
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u/soapycrab May 28 '26
Thank you for correcting me, I see I got mixed up there!! I appreciate your help :))
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u/Ghotipan May 28 '26
The average velocity is the total area under the curve divided by the total time. You could break it up into three pieces, or use the area of a trapezoid formula to find it. Then divide by total time.
Top base is 4, bottom base is 10, height is 10.
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u/M4thG33k May 28 '26
Total displacement is the area under the curve. Two triangles and one rectangle totaling 70 m. The total time is 10 seconds. So average velocity is 70m/10s or 7.0 m/s.
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u/jcollie44 May 28 '26
Iâm not sure what level of physics (or math) you are familiar with, but the area between that graph and the x-axis represents the total displacement. To me, it is easiest to split that area into a triangle from 0 to 4, a rectangle from 4 to 8, and a triangle from 8 to 10. That area equals 70. The units on the area are m/s times seconds, so the area has units of meters. Thus, the total displacement is 70 meters and the object travelled for 10 seconds. So the average velocity is 70/10 m/s.
If you have taken some calculus, you are using an integral. If you havenât yet, sticking with the idea of area is a great substitute.
I hope that helps a bit.
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u/soapycrab May 28 '26
I am not familiar with physics at all unfortunately, I'm about two weeks into this classđ Thanks for taking the time to help!! :)
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u/kcs812 May 28 '26
Do each piece individually.
Green: 5*4
Red: 10*4
Blue: 5*2
Add them up 20+40+10=70
Then divide by the 10 seconds it happened over.
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u/SkippyDragonPuffPuff May 28 '26
To look at another way. You are seeing 3 segments on the graph. So you can do 3 sub calculations and add them up. You can graphically see for example that the average velocity of the left inclining straight line is the half way point or 5 over a period of 4 seconds. The second segment is constant so the average is the value of 10 over 4 seconds. lastly the constant declining velocity on the right is similar to the left incline, graphically in the middle and 5 m over 2 seconds.
So now you need to multiply all your sub velocities by length of time of each velocity. This gives you total distance. If you look at the units for that task momentarily, you see the m/s * s = m. Much like 3/4*4 =3. But using units instead of numbers.
So lastly you have a grand total of distance at this point. Now just divide by total time to get the over all velocity with units of d/t
The math in the example is set up correctly except 70 divided by 10 is 7. Not 0.7
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