Question

an object dropped from rest from the top of a tall building falls y=16t^2 feet first t seconds
(a)find teh speed of a object at t=3s and confirm algebraically

Answer 1

well velocity is just the derivative of the distance equation with respect to time. dy/dt. So the velocty can be determined by 32t evaluated at 3 s= 96 ft/s

Answer 2

hold on i dont know what the derivative is

Answer 3

@Chyme

Answer 4

are you not in calculus? or possibly pre calc?

Answer 5

i am in cal but now we are learning about limits

Answer 6

we did not start derivatives

Answer 7

we can do it another way... since we know that velocity is distance over time the distance can be calculated simply by pluging in a time it into y=16t^2 We want to know the velocity at 3 seconds so we need to know the distances at 3 seconds..16*9=144 ft now you just divide this by the time and you have your velocity =144/3 m/s. This is average velocity and the derivative will give you the instaneous velocity which you will get to soon enough.

Answer 8

ok thx

Answer 9

but the answer was 96

Answer 10

where as 144/3 is 48

Answer 11

It looks like it's asking for instantaneous v.

Answer 12

So if the initial is zero, and the average is 48, what's the final?

Answer 13

have you learned anything like this?

\[\lim_{\Delta x \rightarrow0 } \frac{ f(x+ \Delta x)-f(x) }{ \Delta x }\]

Answer 14

my guess is they want him to use the limit definiton of the derivative to figure out the inst velocity

Answer 15

Maybe, but that's not necessary.

Answer 16

It would be good exercise and a good intro to derivatives, but this is soluble with basic algebra skills.

Answer 17

You already found the average velocity by using (total distance)/(total time), but average velocity (for this particular case since the velocity increases linearly) is also (final + initial)/2.

Answer 18

@ksaimouli, see what i'm saying here? This is an elementary algebra problem. I can show you the calculus necessary to solve it that way, but you don't need it here.