Is the Equation X=ut+1/2at^2 Homogeneous with Respect to Units?

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The equation X=ut+1/2at^2 is homogeneous with respect to units, as all terms can be expressed in consistent units, confirming they are dimensionally equivalent. To determine the magnitude of acceleration from a velocity-time graph, the slope of the straight line represents the acceleration, which is constant in uniformly accelerated motion. For the given graph, the acceleration can be calculated using the formula A = change in velocity/change in time, and any two points on the line can be used for this calculation. Additionally, the distance traveled between specific time intervals can be found by calculating the area under the velocity-time graph. Understanding these concepts is essential for solving related physics problems effectively.
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DEMONSTARTE THAT THE EQUATION X=ut+1/2at2(squared) is homogeneous with repect to units?
how can i use a graph with a streight diagnal line to determine magnitude of acceleration?
 
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faisal said:
DEMONSTARTE THAT THE EQUATION X=ut+1/2at2(squared) is homogeneous with repect to units?
Take each term in that equation and plug in standard units for each variable. Then simplify and compare with each other. (They better all end up with the same units!)
how can i use a graph with a streight diagnal line to determine magnitude of acceleration?
For uniformly accelerated motion, a graph of v (velocity) vs. t (time) will be a straight line whose slope will be the acceleration.
 
I'm not too sure what you mean by homogeneous with respect to units so I'll use the definition for when an ordinary differential equation is homogeneous. Sorry but I don't know TeX too well so try and bear with me as I try to answer this without:

Writing the above equation in differential form, you get

X = dx/dt * t + 1/2 * d^2 x/(dt^2) * t^2

Because all the terms are proportional to X (or one of its derivatives) and beacuse there are no terms without some form of X in them, it is homogeneous.

Edit: nevermind :) Compare units of both sides.

As for the acceleration, you can find the magnitude of the acceleration by taking the instantaneous slope of a velocity-time graph. This graph will be a straight line if acceleration is constant so the slope would be the acceleration.
 
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As for the acceleration, you can find the magnitude of the acceleration by taking the instantaneous slope of a velocity-time graph. This graph will be a straight line if acceleration is constant so the slope would be the acceleration.
the diagram shown in the question is a speed/time graph which shows a constant slope, i don't know how to adress this problem?i don't know how to determine magnetude acceleration,
this is what the question states
a graph shows the speed of a body during time intervals or just over 3 seconds,
(theres a diagram of a small graph with from 0-8ms-1 on the y-axis and 0-8s on the x axis, the graph also shows a slope which appears to be constant.
the question tells me to determine the magnetude of the acceleration?
and to find the distance traveled by the body, between t=6 and t=8.
i'm really struggling.
 
A = change in velocity / change in time . It doesn't really matter which two points you use to calculate the slope since it's linear. Are you currently taking calculus? These problems are trivial if you have at least Calc I under your belt. The position can be determined from a velocity-time graph by taking the area between the time axis and the graph between the two time intervals you said.
 

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