Question

Is the work required to be done by an external force on an object on a frictionless, horizontal surface to accelerate it from a speed $v$ to a speed $2v$

• A. equal to the work required to accelerate the object from t = 0 to v,
• B. twice the work required to accelerate the object from v = 0 to v,
• C. three times the work required to accelerate the object from v = 0 to v,
• D. four times the work required to accelerate the object from 0 to v, or

Answer 1

Answer: (C)

The net work needed to accelerate the object from $v=0$ to $v$ is
$W_1=K{E}_{1f}-K{E}_{1i}$
$=\frac{1}{2}m{v}^2-\frac{1}{2}m(0{)}^2$
$=\frac{1}{2}m{v}^2$
The work required to accelerate the object from speed $v$ to speed $2v$ is
$W_2=K{E}_{2f}-K{E}_{2i}$
$=\frac{1}{2}m(2v{)}^2-\frac{1}{2}m{v}^2$
$=\frac{1}{2}m\left(4v^2-v^2\right)$
$=3\left(\frac{1}{2}m{v}^2\right)=3W_1$