Sketching velocity graph from acceleration graph

In summary, the area under an acceleration vs. time graph represents the velocity. To sketch a velocity vs. time graph, you need to know the initial speed. The graph shows that the acceleration increases to a maximum value, stays constant, then decreases to zero. This means that the velocity is increasing at all times, starting from rest.
  • #1
azn4lyf89
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I know that the area under an acceleration vs. time graph is the velocity, but how do I use that information to sketch a velocity vs. time graph. Is the area considered the slope for the velocity graph? Also how is it possible for a car to be slowing down during the first half of the motion? Attached is a rough sketch of what the acceleration vs. time graph looks like.
 

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  • #2
so on the first thrid of the graph there is constant acceleration so what does this tell you about the velocity?? the middle third there is no acceleration which implies the velocity must be the same. and the last third there is decceleration which implies what about the velocity??
 
  • #3
azn4lyf89 said:
I know that the area under an acceleration vs. time graph is the velocity, but how do I use that information to sketch a velocity vs. time graph.
You need additional information, such as the initial speed.

Note that in this graph, the acceleration increases to a maximum value, stays at that value, then decreases to zero. (Acceleration is only constant in the middle portion of the graph.) If this graph is accurate, and the car starts from rest, the speed is increasing at all times. Is that what you meant to describe?
 
  • #4
RoryP said:
so on the first thrid of the graph there is constant acceleration so what does this tell you about the velocity?? the middle third there is no acceleration which implies the velocity must be the same. and the last third there is decceleration which implies what about the velocity??

Actually, your wrong. The first third of the graph is an increasing acceleration. The second third is a constant acceleration, and the last third is a decreasing acceleration.
 

1. How do I sketch a velocity graph from an acceleration graph?

To sketch a velocity graph from an acceleration graph, you will need to follow a few steps. First, plot the points of the acceleration graph on a graph paper. Then, to find the velocity at each point, integrate the acceleration values. Finally, plot the velocity points on the same graph and connect them with a smooth curve.

2. What is the relationship between acceleration and velocity?

Acceleration is the rate of change of velocity over time. This means that if an object's acceleration is constant, its velocity will change by the same amount every second. Additionally, if an object's acceleration is positive, its velocity will increase, and if the acceleration is negative, its velocity will decrease.

3. Can the velocity be calculated from the acceleration graph directly?

No, the velocity cannot be calculated directly from the acceleration graph. The acceleration graph only shows the rate of change of velocity, not the actual velocity values. To find the velocity, you will need to integrate the acceleration values at each point on the graph.

4. How do I determine the direction of the velocity from an acceleration graph?

The direction of the velocity can be determined by the slope of the acceleration graph. If the slope is positive, the velocity is increasing, and if the slope is negative, the velocity is decreasing. The steeper the slope, the greater the change in velocity over time.

5. Can an object have a constant acceleration and varying velocity?

Yes, an object can have a constant acceleration and varying velocity. This can occur if the acceleration is in the same direction as the initial velocity, causing the velocity to increase. However, as the velocity increases, the acceleration may decrease, causing the velocity to change at a slower rate.

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