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

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 = = displacement

so its not correct

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

This shows slope of position time graph = = velocity

so this is correct for velocity

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

This shows slope of velocity time graph = = acceleration

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

this shows the area of position time graph =

this is no physical quantity

So option B is correct

4

explanation:

4

the independent variable, or the one that is intentionally manipulated is the speed.