Question

The position of a particle moving along the $x$-axis varies with time $t$ as $x=4t-t^2+1$. Find the time interval(s) during which the particle is moving along positive $x$- direction.

• A. $0<t<2$
• B. $t>2$
• C. $t<2$
• D. $t>0$

Answer 1

The correct option is A $0<t<2$

If the particle position in $x$-direction increases with time $t$, then
$\frac{dx}{dt}>0$
$\frac{dx}{dt}=4-2t$
$\frac{dx}{dt}>0\Rightarrow 4-2t>0\Rightarrow t<2$
Hence, the particle moves in positive $x$-direction during the time interval $0<t<2$.