Question

Find the instantaneous velocity and speed at time 5 secs when v(t) = t2 – 9t + 18 and s(0) = 1

Answer 1

i figured i would just ave to find the acceleration (which is just the derivative of v(t)) and then plug five into that but i did that and got it wrong

Answer 2

Why would you find acceleration when it's asking for velocity, just plug in 5 for your velocity.

Answer 3

its asking for the instantaneous velocity doesn't that mean the tangent?

Answer 4

Are you sure it's not suppose to be s(t)

Answer 5

no i am given v(t)

Answer 6

but i am also given s(0) so i can just find s(t)

Answer 7

You're given the instantaneous velocity

Answer 8

Just find v(5)

Answer 9

okay so then v(5) = -2

Answer 10

Yes

Answer 11

okay and for the speed i just find s(t) and plug five into that right?

Answer 12

s(t) is the position

Answer 13

speed is just scalar

Answer 14

okay so then speet(t)=2 ?

Answer 15

Yes, speed is just the magnitude or the velocity

Answer 16

okay lovely ! thank you very much!

Answer 17

Yw :)

Answer 18

We could find the position to s(t), by integrating, \[v(t) = t^2-9t+18 \implies \frac{ ds }{ dt } = t^2-9t+18\]\[\int\limits ds = \int\limits (t^2-9t+18) dt = s(t) = \frac{ t^3 }{ 3 }-\frac{ 9t^2 }{ 2 }+18t+C \]