• $s$$\textcolor{#d64163}{s}$ = displacement

  • if along x-direction , use $\mathrm{\Delta }x$$\Delta x$

  • if along y-direction , use $\mathrm{\Delta }y$$\Delta y$

• $v_i$$\textcolor{#fcc400}{v_i}$ = initial velocity

• $v_f$$\textcolor{#d93ec4}{v_f}$ = final velocity

• $a$$\textcolor{#3A68E8}{a}$ = acceleration

• $t$$\textcolor{#02ccbc}{t}$ = time

• You are driving along at $15.65m/s$$15.65\ m/s$ when suddenly an elephant appears in the middle of the road some distance in front of you.

• Assume your brakes apply an an acceleration of $-4.5m/s^2$$-4.5\ m/s^2$ .

1. What is the distance traveled before you hit the brakes ?

   • Can't be solved !

   • You need to know duration it takes to apply full force of the breaks.

2. What is the distance traveled while you’re slowing to a complete stop ?

• We were not given a time , so start with the equation :

• We know final velocity ( $v_f$$\textcolor{#d93ec4}{v_f}$ ) HAS to be zero.

  • because they said we came to a stop

  • and we are going in the x-direction , so we will replace $s$$s$ with $\mathrm{\Delta }x$$\Delta x$

• They ask us to solve for the distance we travel.

  • "distance we travel" = "displacement" along the x-direction

• So lets rearrange equation to solve for $\mathrm{\Delta }x$$\textcolor{#d64163}{\Delta x}$ :

• Now we can plug numbers in.

• Also note , we are converting negative sign into just $-1$$-1$ ,

  • I think it reads better , and leads to less errors with you have to distributing exponents to parenthesis

• Rewrite / Simplify.

  • "multiplication of the flipped divisor"

  • Careful attention to distribute exponent to EVERYTHING in parenthesis