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A body travels along a straight line wit...

A body travels along a straight line with uniform acceleration ` a_(1)` for time `t_(1)` and with uniform acceleration `a_(2)` for time `t_(2)` for time `t_(2)`. What is the average acceleration?

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Refer to Fig. 2 (b) . 21 , motion from` A to B` is in time ` t_(1)` and from e` B to C` in time `t_(2)`.
.
As change in velocity= accleration
` x time interval`
so,` v_(1) -u =a_(1) t_(1)`
and ` v_(2) -v_(1) =a_(2) t_(2)`
Adding the above equations, we get
`v_(2) -u=a_(1_ t__(1) + a_(2) t_(2)` ..(i)
If ` a_(ac)` is the average acceleration for the motion from ` A to C`, then `
v_(2) -u =q_(av) (t_(1) + t_(2)) `
From (i) and (ii),
` a_(av) (t_(1) + t_(2) =a _(1) t_(1) + a_(2) t_(2)`
:. `a _(av) =(a_(1) t_(1) + a_(2) t_(2))/(t_(1) +t_(2))`.
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