The position of a particle at time t is s(t)=t3+t. Compute the average velocity over the time interval [3,9] and estimate the instantaneous velocity at t=3 I answered the first part, but I dont know how to figure instantaneous velocity.

Question

The position of a particle at time t is s(t)=t3+t. Compute the average velocity over the time interval [3,9] and estimate the instantaneous velocity at t=3  I answered the first part, but I dont know how to figure instantaneous velocity.

anonymous · Answer

to find instantaneous velocity use a figure very close to three. Try using 3.001.

laddiusmaximus · Answer

and then what?

anonymous · Answer

use the slope formula to find the slop between 3 and 3.001

anonymous · Answer

slope*

sriram · Answer

instantaneous vel=3t^2+1
putt=3
to get vel

laddiusmaximus · Answer

so I would plug those in? is that the standard formula format I can use for any problem?

anonymous · Answer

is it 3t or t^3?

laddiusmaximus · Answer

t^3

anonymous · Answer

@Sriram simply plugging in 3 would give you the y-axis position on the velocity.

anonymous · Answer

well, if you use the derivative it would work. Laddius have you started differential equations?

laddiusmaximus · Answer

which i guess is what I need because that was the right answer
so 3(t)^2+1

anonymous · Answer

in other words do you know how to find the derivative of an equation?

sriram · Answer

@ iamtheos the particle ositionb is as a fn of time 
if u differentiate it wid respect to time u get velocity
and i guess the particle is in one dimensional motion

anonymous · Answer

@Sriram the problem being that she may not be able to use Differential Calculus on a test if she is no in a Calculus based class is all i'm saying.

anonymous · Answer

not*

laddiusmaximus · Answer

no im still learning about derivatives
and Im a dude bud. Im in Calc 1

anonymous · Answer

sorry it's getting late here and my typing is getting awful. i meant he. have you learned the product rule? if not you have to use the Average Rate of Change.

laddiusmaximus · Answer

so (t)^2+1 ??

laddiusmaximus · Answer

deltaH/deltaT= s(t1)-s(t2)/t2-t1

laddiusmaximus · Answer

that is average rate of change right?

anonymous · Answer

ARoC is essentially just Y1-Y2/X2-X1 and therefore slope. so take 
$$s(3) = (3)^{3} + 3 = 30$$
and
$$s(3.001) = (3.001)^{3} + 3 = 30.027$$
then
30.027 - 30 "over" 3.001 - 3 which equals 
.027/.001 = 27 which is very close to 30
later on you will learn a simple trick which you can use the 3t^2 +1 equation.

laddiusmaximus · Answer

thanks!!