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velocity vs time and acceleration vs time

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Need help with this problem on position and velocity. I'm given a graph of velocity vs. time, how do I draw the acceleration vs. time from these graph?(question 2) And then I am given acceleration vs. time and need to draw velocity vs. time from these graph (question 3). Please see attachment.

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Solution Summary

In this solution I explain how velocity and acceleration are related and show step by step how you convert a graph of velocity vs time to acceleration vs time (and vice versa).

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Let's start by defining the key terms:
• velocity is the rate at which an object changes its position
• acceleration is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.
Looking at the definitions you can see that velocity and acceleration are related and it is this connectivity which will allow you to develop graphs of acceleration vs time using velocity vs time graphs and vice versa. To think more about this connection consider a car moving with a constant velocity of +10 m/s. Even though the car is moving it is not accelerating. A car moving with a constant velocity has an acceleration of 0 m/s^2. Now consider a car moving with a changing velocity. A car with a changing velocity will have an acceleration.
Now let's think about what the graphs are telling us. To start with velocity vs time: the shape of a velocity versus time graph reveals pertinent information about an object's acceleration. A line sloping up from left to right tells us that the car has a positive velocity (is getting ...

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