Constant Acceleration Problems

we are going to learn how to do constant acceleration problems now when the acceleration is constant that means the value of does not change another way to think about it when the acceleration is constant the velocity is changing by the same amount every second so per second the change in velocity is the same there are four equations of constant acceleration all of these equations indicate that there's acceleration happening when you accelerate you change your velocity you might start at some initial velocity VI and end at final velocity VF and look you see the IV the IV the IV there's only VI here but there's acceleration so the indicates acceleration what about this equation well that equation does not apply to constant acceleration there's only one velocity and they have not said initial or final so this is the equation to use when we have constant velocity not acceleration or if you have an average velocity when there's only one velocity and it's not initial or final that's when we can use this equation so let's say this is our problem this is number two from your homework there are five quantities that are gonna appear in these problems the initial velocity the final velocity the acceleration the displacement and the time let's read the question and see which ones we've been provided with an average acceleration of point eight-six meters per second squared how long will it take cyclist to bring bicycle within an initial speed of nine point one two meters per second to complete stop so what's this value well the unit is meters per second squared so that must be the acceleration and they gave me the direction it's positive okay so the person is accelerating to the right but she's coming to complete stop what does that mean if she's stopping at the end yeah her final velocity is zero her initial speed is nine point one two and don't know the direction right now do because they haven't told me left or right east or west know that this is positive but don't know if this one is positive or negative that'll become clear to us in bit what if they asked me to find how long it takes this amount how long it takes that's like how many seconds it takes they're asking me for the time so find the equation with these four things acceleration final velocity initial velocity and time which one it's this first equation has all four except the last one time that is our unknown quantity so that is still question what is the time we write the equation as it appears and then we plug in the values that were given we're not gonna plug in 40 that's our unknown the final velocity is zero the initial velocity is nine point one two and again don't know yet if it's positive or negative can't think that through just yet well could but I'm struggling and then the acceleration is point eight six subtract nine point one two from both sides it goes away and have point eight six times but wait second when divide both sides by point eight six get negative ten point six seconds as the time time can't be negative so what's going on here this has to be negative initial velocity if the person is traveling to the left but accelerating the other way to the right that's what causes her to come to stop to slow down so to slow down she has to have acceleration and velocity in opposite directions so this has to be opposite in sign to the acceleration okay so now know need to go back and fix my original work because this should have been negative in reality should have been adding 9.12 so my time comes out positive we can now move on to the second part what's the bikers displacement during this time displacement is Delta don't need to list my Givens again they're already above so what do we do we find an equation with Delta and then three of these things we have four but we only need three Givens so there will be couple options I'll use this equation Delta whoops Delta equals one-half VI plus VF times time can plug in the values VI is negative nine point one two VF is zero and the time is I'm going to use the unrounded time ten point six four I'm looking back to my calculator when solve for Delta what do get negative forty eight point four meters notice that I'm putting my answers into three sig figs here and also here all of the Givens had three sig figs this has three this has three and so then have to put my answer to the same number of sig figs