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How to find maximum acceleration in a variable acceleration question?🙏🙏

Heyyyy,

I was doing some variable acceleration questions and I came across this one. I can't find a mark scheme anywhere or anything explaining how to find max acceleration in particular haha.

“A particle P starting from rest moves so that it's velocity v(ms-¹) at time t(s) is v = 12t² - 4t³

(ii) Find the maximum acceleration in the first 2 seconds of motion”

I've differentiated for dv/dt to get the formula for a (a=24t-12t²), but I've no clue how to find where the acceleration is at its highest ?? I've found the acceleration for t=0 and t=2, but surely there's another time you need to find it at? Losing my mind a bit haha, any help would be appreciated.

Thank you :smile:
(edited 11 months ago)
Original post by JRC123
Heyyyy,

I was doing some variable acceleration questions and I came across this one. I can't find a mark scheme anywhere or anything explaining how to find max acceleration in particular haha.

“A particle P starting from rest moves so that it's velocity v(ms-¹) at time t(s) is v = 12t² - 4t³

(ii) Find the maximum acceleration in the first 2 seconds of motion”

I've differentiated for dv/dt to get the formula for a (a=24t-12t²), but I've no clue how to find where the acceleration is at its highest ?? Losing my mind a bit haha, any help would be appreciated.

Thank you :smile:)


So acceleration is a quadratic function of t. Do you know how to find vertex of a quadratic?
(edited 11 months ago)

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