Question - Solving for Initial Velocity and Distance with an Accelerated Motion Formula
Solution:
The given formula is:\[ s = ut + \frac{1}{2}at^2 \]To solve part (a), we want to make $$ u $$ the subject of the formula. Here's how we do it:First, let's rearrange the formula to solve for $$ u $$ by subtracting $$ \frac{1}{2}at^2 $$ from both sides of the equation:\[ s - \frac{1}{2}at^2 = ut \]Next, we divide both sides of the equation by $$ t $$ to solve for $$ u $$:\[ \frac{s - \frac{1}{2}at^2}{t} = u \]So the formula with $$ u $$ as the subject is:\[ u = \frac{s - \frac{1}{2}at^2}{t} \]For part (b), we need to calculate $$ s $$ when $$ a = 100 \text{ m/s}^2 $$, $$ u = 2 \text{ m/s} $$, and $$ t = 5 \text{ s} $$. We can plug the given values into the original formula:\[ s = ut + \frac{1}{2}at^2 \]\[ s = (2 \text{ m/s})(5 \text{ s}) + \frac{1}{2}(100 \text{ m/s}^2)(5 \text{ s})^2 \]\[ s = 10 \text{ m} + \frac{1}{2}(100 \text{ m/s}^2)(25 \text{ s}^2) \]\[ s = 10 \text{ m} + 50(25 \text{ m}) \]\[ s = 10 \text{ m} + 1250 \text{ m} \]\[ s = 1260 \text{ m} \]Thus, the distance $$ s $$ is 1260 meters.
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