Question

A particle leaves the origin at $t=0$ and moves in the positive $x$-axis direction. Velocity of the particle at any instant is given by $v=u(1-\frac{t}{t^{\prime }})$. If $u=10m{s}^{-1}$ and $t^{\prime }=5s$, find the $x$ coordinate of the particle at an instant of $10s$.

• A. $0$
• B. $10m$
• C. $20m$
• D. $-10m$

Answer 1

Answer: (A)

$0$

$v=u(1-\frac{t}{t^{{}^{\prime }}})$

$\Rightarrow \frac{dx}{dt}=u(1-\frac{t}{t^{{}^{\prime }}})$

$\Rightarrow dx=u(1-\frac{t}{t^{{}^{\prime }}})dt$

$\Rightarrow x=u(t-\frac{t^2}{2t^{{}^{\prime }}})$
Put $t=10$ seconds.
$\Rightarrow x=0$