A partical moves in a straight line as `s=alpha(t-2)^(3)+beta(2t-3)^(4)`, where `alpha` and `beta` are constants. Find velocity and acceleration as a function of time.

A partical moves in a straight line as `s=alpha(t-2)^(3)+beta(2t-3)^(4

1.	A partical moves in a straight line as `s=alpha(t-2)^(3)+beta(2t-3)^(4)`, where `alpha` and `beta` are constants. Find velocity and acceleration as a function of time.
Answer» `s=alpha(t-2)^(3)+beta(2t-3)^(4)` `=alpha{(t-2)^(3)}+beta{(2t-3)^(4)}` `v=(ds)/(dt)=alpha.3(t-2)^(2).(1-0)+beta.4(2t-3)^(3).(2.1-0)` `=3alpha(t-2)^(2)+8beta(2t-3)^(3)` `=3alpha{(t-2)^(2)}+8beta{(2t-3)^(3)}` `a=(dv)/(dt)=3alpha.2(t-2).(1-0)+8beta.3(2t-3)^(2).(2.1-0)` `=6alpha(t-2)+48beta(2t-3)^(2)` Recall: First differential the outer layer, then the inner layer and then multiply the two differentials.

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A partical moves in a straight line as `s=alpha(t-2)^(3)+beta(2t-3)^(4)`, where `alpha` and `beta` are constants. Find velocity and acceleration as a function of time.

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