Velocity Time Graph Clarification and Insight Please

[bleedblue1234]

Homework Statement

What type of motion is occurring when the slope is changing and the graph is therefore curved on a velocity time graph?

Homework Equations

v=(delta)x/(delta)t

A= (delta)v/(delta)t

The Attempt at a Solution

my thought is that when the slope is changing the acceleration is either increasing or decreasing ...

So if I were to have an upward sloping curved v-t graph, this would mean that the average acceleration is increasing with time, while if i were to have a downward sloping v-t graph the average acceleration would be decreasing with time...

and if i had a line (linear) slope on a v-t graph, we would have uniform acceleration...

 

[Jebus_Chris]

Yep. The slope of a velocity-time graph is acceleration. So if the function is linear ie slope is constant, then acceleration is constant. It the slope isn't constant you have a changing acceleration.

 

[tomcue]

You are correct in your understanding of the relationship between slope and acceleration on a velocity-time graph. When the slope is changing, this indicates that the acceleration is also changing with time. Depending on the direction of the curve, this can mean either increasing or decreasing acceleration.

In addition, the shape of the curve can also provide insight into the type of motion that is occurring. For example, if the curve is concave upwards (opening upwards), this indicates that the acceleration is increasing with time, which could mean that the object is speeding up. On the other hand, if the curve is concave downwards (opening downwards), this indicates that the acceleration is decreasing with time, which could mean that the object is slowing down.

It is also important to note that the area under the curve on a velocity-time graph represents the displacement of the object. This means that if the curve is curved, the displacement of the object is changing with time, which is indicative of non-uniform motion.

Overall, velocity-time graphs are a useful tool for understanding the motion of an object and how it changes over time. By analyzing the slope and shape of the curve, we can gain valuable insight into the acceleration and type of motion that is occurring.