Question

A particle moves along the x-axis so that its position is given $x=2t^3-3t^2$ at a time $t$ second. What is the time interval during which particle will be on the negative half of the axis?

• A. $0<t<\frac{2}{3}$
• B. $0<0<1$
• C. $0<t<\frac{3}{2}$
• D. $\frac{1}{2}<t<1$

Answer 1

Answer: (C)

$0<t<\frac{3}{2}$

$x=2t^3-3t^2$

When particle is at $-ve$ half of $x$-axis $x<0$

$\therefore$ $2t^3-3t^2<0$

$t^2(2t-3)<0$

$\therefore$ $t^2<0$ and $(2t-3)>0$ Rejected because square of any no. is always positive

$\therefore t^2>0$ and $2t-3<0$

$\Rightarrow$ $t>0$ and $t<\frac{3}{2}$

$\Rightarrow$ $0<t<\frac{3}{2}$