1. what is the kinetic energy of a 150 kg object that is moving with a speed of 15 m/s?\n2. an object has a…

Explanation:

Step1: Recall kinetic - energy formula

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

Question 1

Given $m = 150\ kg$ and $v = 15\ m/s$.

Step1: Substitute values into formula

$K=\frac{1}{2}\times150\times15^{2}$

Step2: Calculate

$K = 75\times225=16875\ J$

Question 2

Given $K = 25\ J$ and $m = 34\ kg$. From $K=\frac{1}{2}mv^{2}$, we can solve for $v$. First, re - arrange the formula to $v^{2}=\frac{2K}{m}$.

Step1: Substitute values

$v^{2}=\frac{2\times25}{34}=\frac{50}{34}\approx1.47$

Step2: Find $v$

$v=\sqrt{\frac{50}{34}}\approx1.21\ m/s$

Question 3

Given $v = 35\ m/s$ and $K = 1500\ J$. From $K=\frac{1}{2}mv^{2}$, we can solve for $m$. Re - arrange the formula to $m=\frac{2K}{v^{2}}$.

Step1: Substitute values

$m=\frac{2\times1500}{35^{2}}=\frac{3000}{1225}\approx2.45\ kg$

Question 4

Given $m = 1200\ kg$ and $v = 24\ m/s$.

Step1: Substitute values into formula

$K=\frac{1}{2}\times1200\times24^{2}$

Step2: Calculate

$K = 600\times576 = 345600\ J$

Question 5

Given $K = 14\ J$ and $m = 17\ kg$. From $K=\frac{1}{2}mv^{2}$, re - arrange to $v^{2}=\frac{2K}{m}$.

Step1: Substitute values

$v^{2}=\frac{2\times14}{17}=\frac{28}{17}\approx1.65$

Step2: Find $v$

$v=\sqrt{\frac{28}{17}}\approx1.28\ m/s$

Answer:

1. $16875\ J$
2. Approximately $1.21\ m/s$
3. Approximately $2.45\ kg$
4. $345600\ J$
5. Approximately $1.28\ m/s$