When acceleration is constant, one equation of kinematics is:
(final velocity)^2 = 2(acceleration)(displacement) + (initial velocity)^2.
When you are graphing this equation with displacement or position of the x-axis and (final velocity)^2 on the y-axis, the equation becomes:
y = 2(acceleration)x + (initial velocity)^2.
Since acceleration is constant, and there is only one initial velocity (so initial velocity is also constant), the equation becomes:
y = constant*x + constant.
This looks strangely like the equation of a line:
y = mx + b.
Therefore, the slope of a velocity squared - distance graph is constant, or there is a straight line.
Now, when you graph a velocity - distance graph, the y axis is only velocity, not velocity squared. So if:
v^2 = mx + b.
Then:
v = sqrt(mx + b). Or: y = sqrt(mx + b).
This equation is not a straight line. For example, pretend m = 1 and b = 0. So the equation simplifies to:
y = sqrt(x).
Now, make a table of values and graph:
x | y
1 | 1
4 | 2
9 | 3
etc.
When you plot these points, the result is clearly NOT a straight line.
Hope this helps!
A graph of distance against time.
To calculate the gradient of the line on a graph, you need to divide the changein the vertical axis by the change in the horizontal axis.
Distance travelled (displacement). Distance = velocity/time, so velocity * time = distance. Likewise, x = dv/dt so the integral of velocity with respect to time (area under the graph) is x, the distance travelled.
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.
To obtain the average velocity from a displacement-time graph, you can calculate the slope of the line connecting two points on the graph. Divide the change in displacement by the change in time. To obtain the instantaneous velocity, you need to find the slope of the tangent line at a specific point on the graph. Choose a point on the graph and draw a line tangent to the curve at that point. The slope of this tangent line will give you the instantaneous velocity at that specific point.
A straight line on a distance - time graph represents a "constant velocity".
It could be a velocity graph or an acceleration graph. If the plot is a straight line it is constant velocity. If the plot is a curve it is acceleration.
distance vs time suggests velocity while distance vs time squared suggests acceleration
The area between the graph and the x-axis is the distance moved. If the velocity is constant the v vs t graph is a straight horizontal line. The shape of the area under the graph is a rectangle. For constant velocity, distance = V * time. Time is the x-axis and velocity is the y-axis. If the object is accelerating, the velocity is increasing at a constant rate. The graph is a line whose slope equals the acceleration. The shape of the graph is a triangle. The area under the graph is ½ * base * height. The base is time, and the height is the velocity. If the initial velocity is 0, the average velocity is final velocity ÷ 2. Distance = average velocity * time. Distance = (final velocity ÷ 2) * time, time is on the x-axis, and velocity is on the y-axis. (final velocity ÷ 2) * time = ½ time * final velocity ...½ base * height = ½ time * final velocity Area under graph = distance moved Most velocity graphs are horizontal lines or sloping lines.
A distance vs time squared graph shows shows the relationship between distance and time during an acceleration. An example of an acceleration value would be 3.4 m/s^2. The time is always squared in acceleration therefore the graph can show the rate of which an object is moving
In a velocity-time graph it will be the time axis (where velocity = 0). On a distance-time graph it will be a line parallel to the time axis: distance = some constant (which may be 0).
A graph of distance against time.
If the axes are time/distance then, and only then, it means a constant velocityIf not, then this Q doesn't have enough data to A
distance = velocity x time so on the graph velocity is slope. If slope is zero (horizontal line) there is no motion
To calculate the gradient of the line on a graph, you need to divide the changein the vertical axis by the change in the horizontal axis.
Distance.
Velocity.