Find the acceleration of an object for which the displacement s (in m) is given as a function of the time t (in s) for the given value of t.

Question

anonymous · Answer

s = 7t3 + 5t2 + 3t - 5, t = 3 s

anonymous · Answer

The answer I came up with was 9490. Am I correct?

phi · Answer

how ?

anonymous · Answer

I substituted 3 for t and solved. I think I misunderstood the question

phi · Answer

displacement is a fancy name for distance  
s (short for "space" the old-fashioned name for distance) is shown as a function of time.
In other words, this equation tells you the distance from the origin at time "t"

velocity (speed) is the change in distance divided by the change in time
or,  the first derivative   ds/dt  

acceleration is the change in velocity with respect to time,  or the 2nd derivative
$$ \frac{d^2s}{dt^2}$$

phi · Answer

so you have to find the 2nd derivative. You do this in two steps
1) find the first derivative
2) now find the derivative of step 1

anonymous · Answer

Okay. I was doing algebra on a calculus question. way off the mark

phi · Answer

the derivative uses the power rule
$$ d x^n = n x^{n-1} $$

anonymous · Answer

Is that the formula used to find the first derivative? I apologize in advance I haven't taken calculus in years

phi · Answer

you have to find the 2nd derivative. You do this in two steps
1) find the first derivative
2) now find the derivative of step 1