Based on the graph, which statement best describes the acceleration of the two objects?
a) acceleration 1 - no acceleration. acceleration 2 - negative acceleration.
b) acceleration 1 - no acceleration. acceleration 2 - speeds up and slows down.
c) acceleration 1 - constant acceleration. acceleration 2 - varied acceleration.
d) acceleration 1 - positive acceleration. acceleration 2 - negative acceleration.

C)Acceleration 1 - constant acceleration. Acceleration 2 - varied acceleration.

Explanation:

In a velocity-time graph, the acceleration corresponds to the slope of the curve.

In fact, acceleration is defined as the ratio between the change in velocity and the time interval:

However, we see that in a velocity-time graph, corresponds to the increment in the y-variable (), while corresponds to the increment in the x-variable (). Therefore, acceleration can also be written as

which is exactly the definition of slope of the curve.

Now we notice that:

- For object 1, the slope is constant: this means that the acceleration is constant

- For object 2, the slope varies: this means that the acceleration varies as well

and 1and 1

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