When is the particle speed up/slowing down

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SUMMARY

The particle's position is defined by the equation s = 2t^2 - 9t^2, leading to a first derivative (velocity) of 6t^2 - 18t and a second derivative (acceleration) of 12t - 18. The particle speeds up when both velocity and acceleration share the same sign and slows down when they have opposite signs. To determine the intervals of speeding up and slowing down, one must find the zeros of the velocity and acceleration equations, specifically at t = 0 and t = 3. Analyzing these intervals will yield the required conditions for the particle's motion.

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Homework Statement



The postion of a particle is given by s=2t^2-9t^2 where t is in seconds and s in meters

a) when is the particle speeding up/slowing down

Homework Equations





The Attempt at a Solution



I have calculated the
1st derivative (velocity) as 6t^2-18t
2nd derivative (acceleration) as 12t-18

and I know that the particle is speeding up when the velocity and the acceleration have the same sign and slowing down when they have opposite signs. However I am not sure how to express this to answer the question.

Thanks
 
Physics news on Phys.org
Find the values of t for which the velocity and for which the acceleration is positive/negative. Hint: They can only change sign at the zeros.
 

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