Question

The quantity jerk, $j$, is defined as the time derivative of an objects acceleration,
$J=\frac{da}{dt}=\frac{d^{3}x}{d{t}^3}$

What is the physical meaning of the area under a graph of jerk versus time?

• A. The area represents the object's change in acceleration.
• B. The area represents the object's acceleration.
• C. The area represents the object's change in velocity.
• D. The area represents the object's velocity.

Answer 1

The correct option is A The area represents the object's change in acceleration.

Area $A$ under a function $f\left(t\right)$ is given by its integral over the variable.

$A={\int }_{t_i}^{t_f}f\left(t\right)dt$

Area under the jerk versus time graph gives,

$A={\int }_{t_i}^{t_f}Jdt$

But, $J=\frac{da}{dt}$

$⟹A={\int }_{t_i}^{t_f}\frac{da}{dt}dt$

$A=\Delta a$

Hence, area under the jerk time-graph gives the change in acceleration.