Question

• always use significant figure rules. remember that these rules apply to all numbers that are measurements.
• in working this problem, assume the value of g to be 9.8 m/s² with two (2) significant digits unless otherwise stated.

if the speed of an object were to triple, what would be the increase of kinetic energy?
ke₂ = ____ ke₁
3
1/9
9
1/3

Explanation:

Step1: Escribir la fórmula de energía cinética

La energía cinética se calcula con la fórmula \( KE=\frac{1}{2}mv^{2} \), donde \( m \) es la masa y \( v \) es la velocidad.

Step2: Calcular \( KE_{1} \) y \( KE_{2} \)

Sea \( v_{1} = v \), entonces \( KE_{1}=\frac{1}{2}mv_{1}^{2}=\frac{1}{2}mv^{2} \). Si la velocidad triplica, \( v_{2} = 3v \), y \( KE_{2}=\frac{1}{2}mv_{2}^{2}=\frac{1}{2}m(3v)^{2}=\frac{1}{2}m\times9v^{2}=9\times(\frac{1}{2}mv^{2}) \).

Step3: Relacionar \( KE_{2} \) y \( KE_{1} \)

Como \( KE_{1}=\frac{1}{2}mv^{2} \) y \( KE_{2}=9\times(\frac{1}{2}mv^{2}) \), entonces \( KE_{2}=9KE_{1} \).

Answer:

C. 9