Question

the ke of a 1000kg satellite is 3 x 10⁶j. if the satellites speed is doubled, the ke will be
▲ 6 x 10⁶j
◆ 12 x 10⁶j
● 16 x 10⁶j
■ 1 x 10⁶j

Explanation:

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy (KE) is $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is speed.

Step2: Analyze Effect of Doubling Speed

Let the initial speed be $v_1$ and final speed be $v_2 = 2v_1$. Initial KE: $KE_1=\frac{1}{2}mv_1^2 = 3\times10^6\,\text{J}$. Final KE: $KE_2=\frac{1}{2}m(v_2)^2=\frac{1}{2}m(2v_1)^2 = 4\times\frac{1}{2}mv_1^2$.

Step3: Substitute Initial KE

Since $KE_1=\frac{1}{2}mv_1^2$, then $KE_2 = 4\times KE_1$. Substitute $KE_1 = 3\times10^6\,\text{J}$: $KE_2 = 4\times3\times10^6 = 12\times10^6\,\text{J}$.

Answer:

$\boldsymbol{12\times10^6\,\text{J}}$ (corresponding to the blue option: $\diamond$ $12\times 10^6$J)