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2.Motion in Straight Line
easy
The velocity of a particle is $v = v _{0}+ gt + Ft ^{2}$. Its position is $x=0$ at $t=0$; then its displacement after time $( t =1)$ is :
A
$v_{0}+g+F$
B
$v_{0}+\frac{g}{2}+\frac{F}{3}$
C
$v_{0}+\frac{g}{2}+F$
D
$v_{0}+2 g+3 F$
(JEE MAIN-2021)
Solution
$v = v _{0}+ g t + Ft ^{2}$
$\frac{ ds }{ dt }= v _{0}+ gt + Ft ^{2}$
$\int ds =\int_{0}^{1}\left( v _{0}+ gt + Ft ^{2}\right) dt$
$s=\left[v_{0} t+\frac{g t^{2}}{2}+\frac{F t^{3}}{3}\right]_{0}^{1}$
$s=v_{0}+\frac{g}{2}+\frac{F}{3}$
Standard 11
Physics
