Im having trouble finding out what the graphs would look like for these kinematic equations
a.v=vox
b.dx=dox + voxt
c. vy=voy +gt
d. dy= doy +voyt +1/2gt^2
can someone explain to me what the graphs would look like and why?
Thanks!!
Sure, I'd be happy to explain what the graphs for these kinematic equations would look like.
a. The equation a.v = vox represents the relationship between acceleration (a) and initial velocity in the x-direction (vox). Since acceleration is the rate of change of velocity, this equation is simply stating that the velocity (v) will change over time (t) with a constant rate of acceleration (a). Therefore, the graph of this equation would be a straight line with a positive slope, indicating a constant acceleration.
b. The equation dx = dox + voxt represents the relationship between displacement (dx) and time (t) in the x-direction. This equation is derived from the definition of velocity as the rate of change of displacement. If we rearrange the equation, we get dx = dox + voxt, which is in the form of y = mx + c, where y represents dx, m represents voxt, x represents t, and c represents dox. This equation represents a straight line with a positive slope (m), indicating a constant velocity in the x-direction.
c. The equation vy = voy + gt represents the relationship between the y-component of velocity (vy), initial y-component of velocity (voy), time (t), and acceleration due to gravity (g). This equation describes the vertical motion of an object under constant acceleration due to gravity. Since gravity is always acting downward, the graph of this equation would be a straight line with a negative slope (equal to the magnitude of acceleration due to gravity -g). The initial y-velocity (voy) represents the y-displacement when time (t) is zero.
d. The equation dy = doy + voyt + 1/2gt^2 represents the relationship between vertical displacement (dy), initial vertical displacement (doy), initial y-velocity (voy), time (t), and acceleration due to gravity (g). This equation describes the vertical motion of an object under constant acceleration due to gravity. The graph of this equation would be a parabolic curve (in the shape of an upside-down U) since it contains a quadratic term (t^2). The initial y-velocity (voy) and the initial vertical displacement (doy) determine the position and shape of the parabola.
In summary, the graphs for these kinematic equations would be:
a. Straight line with a positive slope (constant acceleration).
b. Straight line with a positive slope (constant velocity).
c. Straight line with a negative slope (constant acceleration due to gravity).
d. Parabolic curve (upside-down U) representing the vertical motion under gravity.
I hope that helps! Let me know if you have any further questions.