needs help with 2 differentiation questions

D

DEMONTOSS

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i need help with these problems i tried to differentiate but after that i get stuck on how to use the first derivative.
question 1
a particle moves so that the distance traveled, s metres, in a time t seconds is s= 5 +6t - t^3. calculate the distance at which the body will stop and reverse direction.
question 2
a particle moving in a straight line through 0, so that after t seconds its distance from 0 is given by s= t^3 - 9t^2 +30t. calculate the values of acceleration when the velocity is 6 metres per second
 
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"differentiated line" - You've never heard this term. Try not to invent new language.

"stop and reverse direction." - Something about this language should suggest a 1st derivative. Why?

You should know this:

s(t) gives location.
s'(t) = v(t) gives velocity.
s"(t) = v'(t) = a(t) gives acceleration.

Isn't this in your course materials or classroom notes?
 
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tkhunny said:
"differentiated line" - You've never heard this time. Try not to invent new language.

"stop and reverse direction." - Something about this language should suggest a 1st derivative. Why?

You should know this:

s(t) gives location.
s'(t) = v(t) gives velocity.
s"(t) = v'(t) = a(t) gives acceleration.

Isn't this in your course materials or classroom notes?
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yes okay i kinda have the idea on what do to but when i get the first derivative i kinda get stuck on it like for the first question i get 6-2t^2 as my first derivative which is velocity and i also know since am trying to find the distance where it stops and changes direction velocity is 0 and this is where i get stuck once i equate the first derivative to 0 and these question are from a private study.
 
You say that you need help but you failed to say where you need help. Asking for help in solving a problem and asking for the solution are not the same thing. This is a math help forum where we expect students to solve their own problems with our help.

So you need to give us something to work with. Please read our guidelines, follow them and post back showing us the work you have done so far and where you are stuck.
 
Jomo said:
You say that you need help but you failed to say where you need help. Asking for help in solving a problem and asking for the solution are not the same thing. This is a math help forum where we expect students to solve their own problems with our help.

So you need to give us something to work with. Please read our guidelines, follow them and post back showing us the work you have done so far and where you are stuck.
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i need help on what to do with the first derivative cause i have they idea on how to solve both of them but when i get the first drivative i kinda get stuck on how to move forward from there . for question 1 i know i need to find the time when velocity is zero and take the time found and substitute it in the first equation to get the distance. and for the second question i know need to equate the first derivative to 6 to find the 2 values of t, then take those to values and substitute them in the second derivative to find the values of acceleration but i am stuck at the first derivatives for both question i tried factorizing i failed i tried completing the square to slove for both but i end up with a complex number which is wrong
 
i need help on what to do with the first derivative cause i have they idea on how to solve both of them but when i get the first drivative i kinda get stuck on how to move forward from there

Excellent you found the 1st derivative of some function. So show us your work.
 
i am stuck at the first derivatives for both question i tried factorizing i failed i tried completing the square to slove for both but i end up with a complex number which is wrong

Show us the work, please.
 
DEMONTOSS said:
yes okay i kinda have the idea on what do to but when i get the first derivative i kinda get stuck on it like for the first question i get 6-2t^2 as my first derivative which is velocity and i also know since am trying to find the distance where it stops and changes direction velocity is 0 and this is where i get stuck once i equate the first derivative to 0 and these question are from a private study.
Click to expand...
Why? Did you not study this in your calculus class? That is where you learn to find derivative and differentiate functions. You do not need to factorize for differentiation.
 
DEMONTOSS said:
i need help with these problems i tried to differentiate but after that i get stuck on how to use the first derivative.
question 1
a particle moves so that the distance traveled, s metres, in a time t seconds is s= 5 +6t - t^3. calculate the distance at which the body will stop and reverse direction.[/tex]
The derivative of distance traveled with respect to time is "speed". When an object stops its speed is 0. When it changes direction its speed changes sign- positive to negative or negative to positive.

question 2
a particle moving in a straight line through 0, so that after t seconds its distance from 0 is given by s= t^3 - 9t^2 +30t. calculate the values of acceleration when the velocity is 6 metres per second
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The first derivative is speed (velocity) the second derivative is the acceleration. Take the derivative and set it equal to 6 to find "when the velocity is 6 metres per second". Find the value of the acceleration (second derivative) at that time.
Click to expand...
 
Jomo said:
i am stuck at the first derivatives for both question i tried factorizing i failed i tried completing the square to solve for both but i end up with a complex number which is wrong

Show us the work, please.
Click to expand...
Okay wow i solved the first question for some reason i thought it was giving me a complex number lol it was late when i tired to solve em anyway here is a pic for the second question sorry for bad lighting its early morning
 

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Subhotosh Khan said:
Why? Did you not study this in your calculus class? That is where you learn to find derivative and differentiate functions. You do not need to factorize for differentiation.
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um sorry the first question was my bad i thought i was getting a complex number but i did figure it out so yay and i do now like the end goal but it was just that hurdle that was confusing me
 
i did equal it to 6 and got 2t^2-9t+24 but this is where i get stuck cause i keep getting complex numbers a square root of a negative number
 
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