Question

i need help, I don't know if I'm doing this right...
an object moves with velocity v(t)=t^2-8t+7
a) write a polynomial expression for the position of the particle at any time t greater or equal to zero.
i got 1/3t^3-4t^2+7t+c
b) at what time(s) is the particle changing direction
I got 1 and 7 since i used the v(t) equation...
c) find the total distance traveled by the particle from t=0 and t=4
idk how to do this part without a calculator.

Answer 1

a is good

Answer 2

ok is it set equal to greater or equal to zero?

Answer 3

the particle changes direction at least when v(t) = 0

Answer 4

@amistre64, I agree, which is why t=1 and 7 is the answers for b

Answer 5

c is just telling you to integrate v(t) from 0 to 4

youve already got that in "a" just drop the +c and evaluate it like normal: p(4)-p(0)

Answer 6

the equation in "a" is set to: whatever you want to name the function; p for position maybe?

p(t) = equation in a

Answer 7

ok, so what do i do with the c

Answer 8

since it's asking for the total distance you need to integrate v(t) and find the absolute value from 0 to 4

Answer 9

keep the c to retain generality; any value for c will work

one idea is to make p(0)=0 to match the mehanics of the problem since at time 0 you havent really moved yet

Answer 10

good point dorah; the sign would just indicate direction

Answer 11

so i'd do the absolute value of the (position function at 4 - position function at 0)?

Answer 12

yes

Answer 13

do i have to subtract the the position function at 1 or no

Answer 14

no

Answer 15

ok, so i wanna make sure i have this right, it'd be if i was plugging in 4... 1/3(4)^3-4(4)^2+7(4)

Answer 16

yes, then subtract the value of p(0)

p(4)-p(0)

Answer 17

alright

Answer 18

thank you :)

Answer 19

youre welcome