Question

A $2kg$ object is placed on a horizontal spring and is set into motion. Its position with respect to time is given by the following function:
$x\left(t\right)=0.5\cos \left(10t\right)$
$x\left(t\right)=0.5$ when $t=0$
What is the maximum kinetic energy of the object?

• A. $25J$
• B. $10J$
• C. $5J$
• D. $0.25J$
• E. $0J$

Answer 1

Answer: (A)

$25J$

Position function of the particle $x\left(t\right)=0.5cos\left(10t\right)$ m

Thus velocity of the object $v=\frac{dx\left(t\right)}{dt}=-5sin\left(10t\right)$ m/s

$⟹$Magnitude of maximum velocity $|v_{max}|=5$ m/s

$\therefore$ Maximum kinetic energy $K.E_{max}=\frac{1}{2}m|v_{max}{|}^2=\frac{1}{2}\times 2\times 5^2=25$ J