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Use the position function to find the velocity and acceleration at time t = 2. S(t) = sqrt(t^2 + 8).
 one year ago
 one year ago
Use the position function to find the velocity and acceleration at time t = 2. S(t) = sqrt(t^2 + 8).
 one year ago
 one year ago

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zepdrixBest ResponseYou've already chosen the best response.1
The position function is given by \(\large s(t)=\sqrt{t^2+8}\). The derivative function of position is velocity. \(\large s'(t)=v(t)\). The second dervative of position, which is the first derivative of velocity, is the acceleration function. \(\large s''(t)=v'(t)=a(t)\).
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
So I'll help you along with the first part, I'll bet you can figure out the acceleration based on this. \(\large s'(t)=\dfrac{t}{\sqrt{t^2+8}}\) This is our velocity function, so let's write it like this, \(\large v(t)=\dfrac{t}{\sqrt{t^2+8}}\) They want us to find the velocity at time t=2. \(\large v(\color{royalblue}{2})=\dfrac{\color{royalblue}{2}}{\sqrt{\color{royalblue}{2}^2+8}}\)
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Understand the process? Now take the derivative of your velocity function to find your acceleration function. \(\large v'(t)=a(t)\) and then again, plug t=2 into it to find the acceleration at that time.
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
so i'm taking the derivative of sqrt(t^2 + 8) right? then i plus in 2 ? @zepdrix
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
You/I took the derivative of sqrt(t^2 + 8) to get velocity. Now take the derivative of velocity to get acceleration. So you're now taking the derivative of \[\large v(t)=\dfrac{t}{\sqrt{t^2+8}}\]
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
okay so after i take the derivative of that i subtitute 2 in it right?
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
so i found the derivative of t^2/sqrt(t^2 + 8) and i got 8/t^2 + 8)^3/2 so i substitute the 2 in the t and i got 8/(2^2 + 8)^3/2 which i'm trying to solve now
 one year ago

mathsmindBest ResponseYou've already chosen the best response.1
so whats the problem?
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
i need to solve 8/(2^2 + 8)^3/2 or should i just leave it like that ?
 one year ago

mathsmindBest ResponseYou've already chosen the best response.1
well either u work this out with ur head or use the calculator to get the final answer...
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
I did use the calculation but i'm not getting a right answer
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
@zepdrix i'm stuck on this one can u help?
 one year ago

mathsmindBest ResponseYou've already chosen the best response.1
\[s(t) = \sqrt{t^2 + 8}\] \[v(t)=\frac{t}{\sqrt{t^2+8}}\] \[a(t) = \frac{1}{(t^2+8)^{\frac{1}{2}}}\frac{t^2}{(t^2+8)^{\frac{3}{2}}}\]
 one year ago

mathsmindBest ResponseYou've already chosen the best response.1
now solve for v(2), and a(2) you'll get the answer
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
so i should subtitute 2 into t?
 one year ago

mathsmindBest ResponseYou've already chosen the best response.1
\[v(2)=\frac{(2)}{\sqrt{(2)^2+8}}\]
 one year ago

mathsmindBest ResponseYou've already chosen the best response.1
\[v(2)=\frac{2}{2\sqrt{1+2}}=\frac{1}{\sqrt{3}}\]
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
what does m.s 1 mean?
 one year ago

mathsmindBest ResponseYou've already chosen the best response.1
it means meter per a second, u have to put units
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
so bow i have to solve the problem above?
 one year ago

mathsmindBest ResponseYou've already chosen the best response.1
\[a(2) = \frac{1}{((2)^2+8)^{\frac{1}{2}}}\frac{(2)^2}{((2)^2+8)^{\frac{3}{2}}}\]
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
okay so i need to solve that
 one year ago

mathsmindBest ResponseYou've already chosen the best response.1
but u really need to know how to differentiate those simple equations ok
 one year ago
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