Question

The area of the acceleration-displacement curve of a body gives :

• A. impuse
• B. change in momentum per unit mass
• C. change in KE per unit mass
• D. total change in energy

Answer 1

Answer: (C)

change in KE per unit mass

The area of the acceleration $\left(a\right)$ - displacement $\left(x\right)$ curve will be

$A=\int adx=\int \frac{dv}{dt}dx=\int dv\frac{dx}{dt}=\int vdv$

If we integrate this with limit $v_1$ to $v_2$, we will get $A=\frac{1}{2}(v_2^2-v_1^2)$

This is the change in kinetic energy of the body per unit its mass.

Thus option C is correct.