How to draw a qualitative a vs. t graph

[swimmer59]

how to draw a "qualitative a vs. t graph"

So basically, we just started learning about acceleration and my teacher gave us this worksheet but we haven't learned anything yet. it shows a sketch of a ball rolling down a hill. gives x0=0cm v0=o m/s. and the other sketch is a ball rolling down a hill but in the negative direction. so x0> 0cm and v0=0m/s.
there is no other info just what i gave.3. i know the x vs t graphs are a parabola and the v vs t graphs are a linear line. but i am confused what the a vs t graphs would look like.

 

[fss]

i know the x vs t graphs are a parabola and the v vs t graphs are a linear line. but i am confused what the a vs t graphs would look like.

A ball rolling down a hill (at the level you're learning) is basically in free fall. What do you know about objects in free fall- does their acceleration change?

 

[swimmer59]

no i believe they have a constant acceleration. right?

 

[fss]

Right. That's a major clue about the shape of the acceleration vs. time plot.

 

[rwisz]

I would first commend you for actively seeking clarification on a topic that you are unsure about. It is important to understand the fundamentals before moving on to more complex concepts.

To draw a qualitative a vs. t graph, we first need to understand what acceleration represents. Acceleration is the rate of change of velocity over time. In other words, it measures how quickly an object is changing its velocity.

In your example, the first sketch shows a ball rolling down a hill with an initial position (x0) of 0 cm and an initial velocity (v0) of 0 m/s. This means that the ball is not moving at the start and will gradually gain speed as it rolls down the hill. The second sketch shows the ball rolling down the hill in the negative direction, which means it is rolling uphill. In this case, the initial position (x0) is greater than 0 cm and the initial velocity (v0) is 0 m/s. This means that the ball is moving in the opposite direction and will gradually decrease in speed as it moves uphill.

Now, to draw a qualitative a vs. t graph, we need to plot the acceleration of the ball on the y-axis and time on the x-axis. Since the ball is initially at rest in both sketches, the acceleration at the start is 0 m/s^2. As the ball starts to roll down the hill in the first sketch, the acceleration will increase in a positive direction, meaning the ball is gaining speed. This would be represented by a positive slope on the a vs. t graph. In the second sketch, as the ball rolls uphill, the acceleration will decrease in a negative direction, meaning the ball is slowing down. This would be represented by a negative slope on the a vs. t graph.

In summary, a qualitative a vs. t graph for a ball rolling down a hill would show a positive slope as the ball gains speed and a negative slope as it slows down. It is important to note that this is a very simplified explanation and in reality, the a vs. t graph would be a curve, as the acceleration is constantly changing. I hope this helps to clarify how to draw a qualitative a vs. t graph.