Question

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

Answer 1

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 = $\frac{ds}{dt}$ = velocity

so this is correct for velocity

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

This shows slope of velocity time graph = $\frac{dv}{dt}$ = 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

Answer 2

Answer: C

Explanation: