Chapter 3, Problem 9STP

To determine

To Choose: The correct option.

Answer to Problem 9STP

Correct option is D.

Explanation of Solution

Introduction:

Acceleration is defined as the rate of change of velocity.

  $a=\frac{dv}{dt}$

Instantaneous acceleration is defined as the acceleration of an object at any instant of time during its motion.

Instantaneous acceleration is equal to the limiting value of the average acceleration as $\Delta \text{t}\to \text{0}$

Therefore, Instantaneous acceleration

  $\begin{array}{l}a=\underset{\Delta t\to 0}{Lt}\left(a_{av}\right)\\ a=\underset{\Delta t\to 0}{Lt}\frac{\Delta v}{\Delta t}\\ a=\frac{dv}{dt}\end{array}$

Option (A) is not correct as the slope of position time graph represents velocity not acceleration.

Option (B) is not correct as the area under position time graph describes the answer with unit $\text{m}\cdot \text{s}$ which is meaningless.

Option (C) is incorrect as the area under the velocity − time graph represents the displacement of the object.

Option (D): is correct as the slope of velocity time graph represents acceleration.

Conclusion:

D is the correct option.