Question

the aacelration of an object varies as a=tsquare+2t+1m/s.if the initial velocity of an object is 2m/s . calculate it's velocity at t= 4sec​

Answer 1

$\longrightarrow Given :-$

$a = t^2+2t+1 m/s^2$

$u = 2m/s$

$t = 4sec$

$\longrightarrow To\:Find :-$

$Final \: velocity$

$\longrightarrow SOLUTION:-$

$As\: they\: given \\a= t^2+2t+1$

$Substitute \: value\: of \: t$

$We \: can \: get \: the \: acceleration \: of \: the\: body$

$At\:t = 4m/s^2$

$a = (4)^2+ 2(4) +1$

$a = 16+8+1$

$a = 25m/s^2$

$u = 2m/s$

$t = 4 s$

$v =?$

$We\: know\: that$

$a =\dfrac{v-u}{t}$

$Substituting \: the \: values$

$25 = \dfrac{v- 2}{4}$

$25(4) = v-2$

$100 = v-2$

$v = 100+2$

$v = 102m/s$

$So\: the\: final \:velocity \: is\: 102m/s$