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Let's assume we have an object moving in the x-direction alone, calling its position x(t), where t is time.; and imagine it has constant acceleration a. Acceleration is the second derivative of time - in terms of calculus,
d2x/dt2 = a. (1)
So we can get the graph of the position by integrating (1). Doing this once gives us the velocity:
dx/dt = at + C
where, if the initial velocity (the velocity at time t = 0) is given by u and we substitute this in, we get
u = a*0 + C so that C = u, giving
dx/dt = at + u (2)
Now to get the solution for the position of the object against time, we integrate (2):
x(t) = (1/2)*at2 + ut + D
And, if the position of the object at time t = 0 is just called x(0), we get
x(0) = (1/2)*a*02 + u*0 + D so that D = x(0), finally giving
x(t) = (1/2)*at2 +ut + x(0) (3)
(3) you might recognise as the general equation of motion of an object with constant linear acceleration. Note that it is a quadratic function, and so is generally shaped like a parabola (See 'parabola', under wiki; [http://en.wikipedia.org/wiki/Parabola] especially the top-most line drawing (although imagine it upside down as the track of a ball thrown upwards, under the constant acceleration of gravity) and also the picture of the bouncing tennis ball at the bottom, each period in the air is an example of a parabolic track.)
Final point - note that the parabola (in projectile motion cases) -always- has a curve leading up from the ground and then back down. Sounds obvious, i know; but recall that objects moving under gravity are measured as having a -negative- acceleration, hence the first term of the quadratic is negative,the parabola will be upturned compared to a graph like x = t2. Hope this helps ;)
Wiki User
∙ 15y ago
Wiki User
∙ 7y agoThat really depends on the specific graph.
Jacob Miller
Wiki User
∙ 11y agoA straight line that coincides with the time axis, i.e., its value is zero at any time.
Wiki User
∙ 11y agoUniform motion is represented by a straight line.
Wiki User
∙ 16y agoIt will plot as a straight line.
Wiki User
∙ 6y agowhen you graph the motion of an object
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How Can you tell from a velocity-time graph that the velocity is constant?
velocity is nothing but speed of a body in the given direction. suppose if body is moving with constant velocity then VT graph will be parallel to the X -axis, if not then the VT graph is not parallel to the X-axis it means then object is moving with different velocity or it has its dierection or both velocity and aswell as direction.
A graph showing zero slope for the position vs time always indicates that the object is not moving?
If the speed/time graph slops negatively, that's an indication that the speed is decreasing, i.e. the object is slowing down. The negative slop is also called negative acceleration, since acceleration is the rate of change of velocity.
What information can be learned from a position-time graph and from a speed-time graph?
A position time graph can show you velocity. As time changes, so does position, and the velocity of the object can be determined. For a speed time graph, you can derive acceleration. As time changes, so does velocity, and the acceleration of the object can be determined.If you are plotting velocity (speed) versus time, the slope is the acceleration.
What does slope of position time graph represents?
It represents the velocity of the object.
What is the slope of the line tangent to the curve on a position-time graph at a specific time?
The slope of the tangent line in a position vs. time graph is the velocity of an object. Velocity is the rate of change of position, and on a graph, slope is the rate of change of the function. We can use the slope to determine the velocity at any point on the graph. This works best with calculus. Take the derivative of the position function with respect to time. You can then plug in any value for x, and get the velocity of the object.
Can you tell from a velocity-time graph whether an object is stationary?
If the curve is horizontal, then the speed is constant. If that horizontal graph lies on the x-axis, then the constant speed is zero, and the object is stationary.
How Can you tell from a velocity-time graph that the velocity is constant?
velocity is nothing but speed of a body in the given direction. suppose if body is moving with constant velocity then VT graph will be parallel to the X -axis, if not then the VT graph is not parallel to the X-axis it means then object is moving with different velocity or it has its dierection or both velocity and aswell as direction.
Can you tell from a displacemnt-time graph wheather an object is stationary?
Of course yes. An object is stationary when the graph is horizontal in a displacement-time graph.
A graph showing zero slope for the position vs time always indicates that the object is not moving?
If the speed/time graph slops negatively, that's an indication that the speed is decreasing, i.e. the object is slowing down. The negative slop is also called negative acceleration, since acceleration is the rate of change of velocity.
Does a vertical line on a distance time graph indicate that an object is stationary?
Object will change distance time graph when speed is changing. Distance time graph don't changed indicate of the stationary.
What variable does slope represent in a velocity vs time graph?
The Physical quantity that the slope of velocity time graph show is:negative acceleration otherwise retardation.If the velocity of the body is decreasing then the body is said to have negative acceleration (-ve) or retardation.u>v
What is the y-intercept of the velocity time graph?
The velocity of the object at time = 0
What can you say about the motion of an object whose distance time graph is a straight line parallel to time axis?
The object is stationary as its velocity is zero. The velocity of an object is the gradient of its distance-time graph and as the graph is a horizontal straight line, its gradient is zero. The object is stationary also as its distance from the time axis is not increasing.
What is a negative slope on a velocity-time graph indicates the object is down?
A negative slope on a velocity-time graph indicates a decreasing velocity over time, which means the object is slowing down. As time increases, the velocity decreases.
What information can be learned from a position-time graph and from a speed-time graph?
A position time graph can show you velocity. As time changes, so does position, and the velocity of the object can be determined. For a speed time graph, you can derive acceleration. As time changes, so does velocity, and the acceleration of the object can be determined.If you are plotting velocity (speed) versus time, the slope is the acceleration.
What does the area under an acceleration time graph show?
The area under an acceleration-time graph is equal to the object's velocity (not change in velocity).
What is the physical property represented by the slope of a distance time graph?
The velocity. To convince yourself, consider the units of the slope. Slope = rise/run = vertical/horizontal= distance/time=units of velocity. Alternately, consider the meaning of the graph. Where the slope is high, the distance is changing fast over a small time - high velocity.
