Question

a physics student monitors the speed and kinetic energy of a 0.48 kg traveling object. at a time of t = 1.0 s, the object is traveling with a speed of 6.0 m/s and at a time of t = 4.0 s, the object has a kinetic energy of 20 j. determine the following. (a) the kinetic energy of the object (in j) at t = 1.0 s (b) the speed of the object (in m/s) at t = 4.0 s

Explanation:

Step1: Recall kinetic - energy formula

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

Step2: Calculate kinetic energy at $t = 1.0\ s$

Given $m = 0.48\ kg$ and $v=6.0\ m/s$. Substitute into the formula: $K=\frac{1}{2}\times0.48\times(6.0)^{2}=\frac{1}{2}\times0.48\times36 = 8.64\ J$.

Step3: Recall kinetic - energy formula for part (b)

We know $K=\frac{1}{2}mv^{2}$, and we want to find $v$. Rearranging the formula for $v$, we get $v=\sqrt{\frac{2K}{m}}$.

Step4: Calculate speed at $t = 4.0\ s$

Given $K = 20\ J$ and $m = 0.48\ kg$. Substitute into the formula: $v=\sqrt{\frac{2\times20}{0.48}}=\sqrt{\frac{40}{0.48}}\approx\sqrt{83.33}\approx9.13\ m/s$.

Answer:

(a) $8.64$
(b) $9.13$