I need to know how to graph this equation to form a straight line:
x = 1/2at^2
I would graph x versus t^2 but is that correct?
Thank you very much!
Sure, that will work.
You could also use a sheet of graph paper with log scales.
log x = log [.5 a t^2] = log(.5 a) + 2 log t
To graph the equation x = 1/2at^2 and form a straight line, you need to follow the steps listed below:
1. Rearrange the equation to isolate x: Start by multiplying both sides of the equation by 2 to remove the coefficient 1/2. The equation becomes 2x = at^2.
2. Divide both sides of the equation by a: Divide both sides of the equation by a to isolate t^2. The equation simplifies to (2x)/a = t^2.
3. Take the square root of both sides: To eliminate the squared term, take the square root of both sides of the equation. Remember to consider both positive and negative square roots. The equation becomes √((2x)/a) = t.
Now that you have isolated t, you can plot the graph by considering x as the dependent variable and t as the independent variable.
- Choose a range of values for t: Select a range of values for t, such as -10 to +10 or any other range that includes the desired portion of the graph.
- Substitute the values of t into the equation: Plug each value of t into the equation √((2x)/a) = t to calculate the corresponding values of x.
- Plot the points: Use the calculated values of x and t to plot points on a coordinate plane with x on the vertical axis and t on the horizontal axis.
- Connect the points: Once you have plotted multiple points, draw a straight line connecting them. This line represents the graph of x = 1/2at^2.
Keep in mind that the graph will vary depending on the value of the coefficient a. If a is positive, the graph will open upward, and if a is negative, it will open downward. Also, note that the graph will start at the y-intercept (0, 0) since x = 0 when t = 0.