Question

The position of a particle moving along x-axis varies with time $t$ as $x=4t-t^2+1$. If the time interval(s) during which the particle is moving along positive x-direction is $0<t<u$. The value of $u$ (in $s$) is

Answer 1

If the particle position in $x$- direction will increase 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 time-interval 0-2 sec.

$\Rightarrow u=2$