Acceleration 'a' in m/{s^2} of a particle is given by a = 3{t^2} + 2t + 2 where t is time. I

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2.Motion in Straight Line

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The acceleration $'a'$ in $m/{s^2}$ of a particle is given by $a = 3{t^2} + 2t + 2$ where $t$ is the time. If the particle starts out with a velocity $u = 2\,m/s$ at $t = 0$, then the velocity at the end of $2$ second is.......$m/s$

A$12$

B$18$

C$27$

D$36$

Solution

(b) $ v = u + \int_{}^{} {adt = u + \int_{}^{} {(3{t^2} + 2t + 2)dt} } $
$ = u + \frac{{3{t^3}}}{3} + \frac{{2{t^2}}}{2} + 2t = u + {t^3} + {t^2} + 2t$
$ = 2 + 8 + 4 + 4 = 18\;m/s$ (As $t = 2\, sec$)

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The acceleration $'a'$ in $m/{s^2}$ of a particle is given by $a = 3{t^2} + 2t + 2$ where $t$ is the time. If the particle starts out with a velocity $u = 2\,m/s$ at $t = 0$, then the velocity at the end of $2$ second is.......$m/s$

Solution

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