Starting at t = 0, a particle moves along a line so that its position, in metres, after t
seconds, is given by s(t) = t2 − 7t + 6. Find the velocity of the particle when its position
is 14

Question

Starting at t = 0, a particle moves along a line so that its position, in metres, after t
seconds, is given by s(t) = t2 − 7t + 6. Find the velocity of the particle when its position
is 14

campbell_st · Answer

let s(t) = 14 and then solve the quadratic. 

this will give the time(s) when the particle is 14 from the origin. 

next

find the 1st derivative, when you have that equation substitute your value(s) of t to find the velocity when the particle is 14 from the origin.

anonymous · Answer

when i solve the quadratic i get, t = 15... is that right?

campbell_st · Answer

well you have to solve 

14 = t^2 - 7t + 6

or 

t^2 - 7t - 8 = 0

anonymous · Answer

yeah... i'm still getting 15

anonymous · Answer

At least you can factor it !!!

anonymous · Answer

lol

campbell_st · Answer

ok... do you know how to solve a quadratic..?

anonymous · Answer

well apparently not. i thought i did... :(

campbell_st · Answer

so factors of -8.. any thoughts..?

anonymous · Answer

are they not 1, 2, 4, and eight?

anonymous · Answer

oh pellet, hold on i think i got it

anonymous · Answer

nope nevermind...

campbell_st · Answer

well you need -8... not 8... and then you need to find the 2 factors that then add to - 7

campbell_st · Answer

so you can use -2 x 4, 2 x -4 , -1 x 8 or 1 x -8...

anonymous · Answer

(t - 8)(t - 1)

anonymous · Answer

i mean t + 1

campbell_st · Answer

nope... that gives t^2 - 9t + 8 = 0

its actually

(t - 8)(t + 1) = 0

so only consider the solution t = 7 as time can't be negative. 

so the particle is 14 from the origin when t = 7

so can you find the 1st derivative...?

anonymous · Answer

2t - 7 ?

campbell_st · Answer

thats good, the 1st derivative is the rate of change in displacement... or the velocity equation. 

so to find the velocity when the particle is 14 from the origin... substitute t = 7 into the 1st derivative.

anonymous · Answer

then i'll get 2(7) - 7, which is 14

anonymous · Answer

but the answer is 9... unless i messed up somewhere...

campbell_st · Answer

2 x 7 -  7 isn't 14

anonymous · Answer

i meant 7 lol

anonymous · Answer

don't know what i was thinking.

anonymous · Answer

oh i was supposed to use t = 8, not 7

campbell_st · Answer

oops you need to substitute t = 8... not t = 7.... 

t = 8 is a solution to (t -8)(t+1) = 0

so the velocity is  2(8) - 7 = 9 units per second

anonymous · Answer

thank you