Math and Arithmetic
Physics
Kinematics

# How is instantaneous acceleration related to a velocity-time graph?

Acceleration is the derivative of velocity (a=dv/dt). If you are not familiar with calculus then it would be sufficient to say that the slope of the line tangent to the graph, only touches at one point, is equal to the instantaneous acceleration.

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## Related Questions

The slope of a velocity-time graph that shows uniform acceleration is the actual acceleration. Instantaneous velocity is the velocity of a body at a particular moment in time.

Yes it does. Better call it instantaneous acceleration.

Besides obviously distance at any instant, on a connected, continuous distance-time graph, you can obtain instantaneous velocity and instantaneous acceleration.

The average acceleration can be obtained by finding the slope of the graph. The instantaneous acceleration is found by drawing a tangent to a particular point on the graph (instant) and finding the slope of than tangent.

Instantaneous acceleration... Slope of the tangent to a velocity time graph at any point is of the form velocity/time=acceleration.

When there is no acceleration or when there is constant acceleration. When either of these cases is present, the graph of velocity versus time will be linear. When there is linear velocity, the average velocity will equal the instantaneous velocity at any point on the graph.

The slope of a distance versus time graph provides the instantaneous speed of an object. If data from this graph is then used to construct a speed versus time graph, the slope of that graph would provide the instantaneous acceleration.

With great difficulty since the question does not specify what aspect of the object's instantaneous. Speed, position, acceleration?

The acceleration. If the slope is only at a certain point then it's instantaneous acceleration and if the slope is made from two points then it's an average acceleration.

instantaneous acceleration* * * * *No it does not.The graph is a distance-time graph so the coordinates of a point on the graph represent the position (distance) at the specified time. The gradient of the tangent to the curve at that point represents the instantaneous radial velocity. The second derivative at that point, if it exists, would represent the acceleration.

acceleration is the slope of the velocity graph. acceleration is also the derivative of velocity.

If your graph shows velocity on the vertical axis and time on the horizontal axis, then the slope of the graph represents the acceleration. More specifically, the slope of the graph at a specific point represents the acceleration at that instantaneous point in time. So if the slope of the graph doesn't change (i.e. the graph is a straight line), then the acceleration is constant and doesn't change over time. In calculus, this is represented as the derivative: The derivative of velocity with respect to time equals the acceleration.

5. A particle is moving along the x-axis. The line graph shows the velocity of the particle over time. When is the instantaneous acceleration of the particle equal to 0?

No. Velocity is displacement divided by time. Acceleration is velocity divided by time. However both graphs are related! If you graph the AREA under the slope of the acceleration graph vs. time, this will be a velocity graph. If you graph the SLOPE of the velocity graph vs. time, this will be an acceleration graph. When you learn calculus (unless you already know it) you will learn how you can switch between the two.

a=dv/dt=d/dt(dx/dt)=d^2x/dt^2Is the rate of a tangent to the slope of a graph signifying velocity versus time. It is a snapshot of acceleration at a precise moment in time based on the relative changes in velocity over time. It is the limit of acceleration for any given point within the displacement vector.Instantaneous acceleration is how fast a velocity is changing at a specific instant.

A graph that shows speed versus time is not an acceleration graph.The slope of the graph at any point is the acceleration at that time.A straight line shows that the acceleration is constant.

The answer depends on what is plotted on the graph and what is happening with the acceleration then.

The answer depends on the variables in the graph! In a graph of age against mass there is nothing that represents acceleration.

This depends on what the graph represents. If it is a graph of velocity on the vertical and time on the horizontal, then if acceleration is at a constant rate, the graph will be a straight line with positive slope (pointing 'up'). If acceleration stops, then the graph will be a horizontal line (zero acceleration or deceleration). If it is deceleration (negative acceleration), then the graph will have negative slope (pointing down).

Yes. Free fall can be graphed on a position-time graph and a velocity-time graph. Refer to the related link below for examples.

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