Question

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

Answer 1

Answer: C

Step-by-step explanation:

Answer 2

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