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2.Motion in Straight Line
medium
The velocity $v$ of a particle is given by the equation $v = 6t^2 -6t^3$, where $v$ is in $m/sec$ and $t$ is time in $seconds$ then
A
at $t = 0$, velocity is maximum
B
at $t = \frac{2}{3}$, velocity is minimum
C
minimum velocity is zero
D
minimum velocity is $-2\, m/sec$
Solution
$\frac{\mathrm{d} \mathrm{V}}{\mathrm{dt}}=12 \mathrm{t}-18 \mathrm{t}^{2}=0 \Rightarrow \mathrm{t}=0,2 / 3$
$\frac{\mathrm{d}^{2} \mathrm{V}}{\mathrm{dt}^{2}}=12-36 \mathrm{t}>0 \Rightarrow$ for $\mathrm{t}=0$ so $\mathrm{v}_{\min }$ will be at
$t=0$
Standard 11
Physics
