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Which of the following numbers is equal to an object's acceleration?

A. The area under that object's velocity-time graph
B. The slope of that object's position-time graph
C. The slope of that object's velocity-time graph
D. The area under that object's position-time graph

User Bryce York
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2 Answers

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Answer: C

Step-by-step explanation:

User Bojan Bjelic
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For the given all options we can find the respective quantity

whenever we have to relate slope of a graph then it is always derivative of quantity on Y axis with respect to X axis

while if we need to find the area of the graph then it is integral of quantity on Y axis with respect to x axis

A. The area under that object's velocity-time graph

this shows area of velocity time graph =
\int v dt = displacement

so its not correct

B. The slope of that object's position-time graph

This shows slope of position time graph =
(ds)/(dt) = velocity

so this is correct for velocity

C. The slope of that object's velocity-time graph

This shows slope of velocity time graph =
(dv)/(dt) = acceleration

D. The area under that object's position-time graph

this shows the area of position time graph =
\int s dt

this is no physical quantity

So option B is correct

User ThreeAccents
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