Question

1. a 2 kg object has a kinetic energy of 2j when its speed is (a) 0.457 m/s (b) 1.0 m/s (c) 1.414 m/s (d) 2.0 m/s (e) none of the above

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $K = \frac{1}{2}mv^{2}$, where $K$ is the kinetic energy, $m$ is the mass, and $v$ is the speed. We need to solve for $v$.

Step2: Rearrange the formula for $v$

Starting from $K=\frac{1}{2}mv^{2}$, we can first multiply both sides by 2 to get $2K = mv^{2}$. Then divide both sides by $m$: $v^{2}=\frac{2K}{m}$. Taking the square - root of both sides gives $v=\sqrt{\frac{2K}{m}}$.

Step3: Substitute given values

We are given that $K = 2J$ and $m = 2kg$. Substituting these values into the formula $v=\sqrt{\frac{2K}{m}}$, we have $v=\sqrt{\frac{2\times2}{2}}=\sqrt{2}\approx1.414m/s$.

Answer:

C. 1.414 m/s