Checkpoint: Physics Applications of Rational Equations Solution

Brian and Steven were sledding down a hill. Brian gave Steven’s sled a push such that his initial velocity was 3 m/s. He accelerated down the hill at 4 m/ $s^{2} .$ Steven traveled 40 meters down the hill.

Substitute the known values into the equation: $\frac{2 ∆ x}{v_{f} + v_{i}} = \frac{v_{f} - v_{i}}{a}$

And set it equal to zero. Do not solve.

$\begin{array}{rcl} v_{i} & = & 3 \frac{m}{s} \\ a & = & 4 \frac{m}{s^{2}} \\ ∆ x & = & 40 \end{array}$

$\begin{array}{rcl} \frac{2 (40)}{v_{f} + 3} & = & \frac{v_{f} - 3}{4} \\ (v_{f} + 3) (v_{f} - 3) & = & 2 (4) (40) \\ v_{f}^{2} - 9 & = & 320 \\ v_{f}^{2} - 329 & = & 0 \end{array}$

Note

You do not need to solve this equation. The biggest challenge in this type of problem is correctly identifying the given values and correctly substituting in the values to the formula.

Q: Why is it important to identify the given values for a formula?
A: So you know what values you have and what you need to solve for.

Q: If you were required to solve, what value would you solve for?
A: The final velocity, $v_{f}$ .

Remember from Algebra 1 that it is possible to solve the equation $v_{f}^{2} = 329$ by taking the square root of both sides. The result is approximately $\pm 18 \frac{m}{s}$ where $- 18 \frac{m}{s}$ is extraneous.