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AP.CALC:

CHA‑4 (EU)

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, CHA‑4.C.1 (EK)

divya received the following problem a particle moves in a straight line with velocity V of T is equal to the square root of 3 t minus 1 m/s where T is time in seconds at T equals 2 the particles distance from the starting point was 8 meters in the positive direction what is the particles position at T equals 7 seconds which expression should Divya use to solve the problem so pause this video and have a go at it alright now let's do this together so we want to know the particles position at T is equal to 7 so what we could do they tell us what our position is at T equals 2 so what the position at T equals 7 would be your position at T equals 2 plus your change in position from T equals to 2 T is equal to 7 and there's another word for this you could also call this your displacement from T equals to 2 T equals 7 and we know how to think about displacement velocity is your rate of change of displacement and so if you want to figure out your displacement you're between two times you would integrate the velocity function so this is going to be the integral from T equals to 2 T equals 7 of our velocity function V of T DT this would be our displacement from time to 2 times 7 so if they said what is our change in position from time to 2 times 7 it would be just this expression but they want to they want us to figure out or they want Divya to figure out what is the particles position at T equals 7 seconds so what you would want to do is your position at T equals 2 and we know at our position at T equals 2 is it was 8 meters in the positive direction so we could just call that positive 8 meters so it's going to be 8 plus your change in position which is going to be your displacement and let's see we can see this choice right over there and that's what we would pick this first option V of 7 that just gives us our velocity at time seven or at exactly at seven seconds or another way our rate of change of displacement at seven seconds so that's not what we want this one right over here you have your position at T equals two but then you have your change in position from T equals zero to T equals seven so this doesn't seem this isn't right and this is your position at time two plus your V Prime the derivative of velocity is the acceleration plus your acceleration at time seven so that's definitely not going to give you your the particles position so we like that second choice

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