Question

A body of mass $0.4\, kg$ starting at origin at $t = 0$ with a speed of $10 \,m \s$ in the positive $x$-axis direction is subjected to a constant $F = 8\, N$ towards negative $x$-axis The position of the body after $25\, s$ is

• A. $-6000 \, m$
• B. $-8000 \, m$
• C. $+4000 \,m$
• D. $+7000 \,m$

Answer 1

Answer: (A)

$-6000 \, m$

Answer 2

Here, Mass of the particle, $m = 0.4 \,kg$
$F = -8 \,N$(minus sign for direction of force)
$\therefore\quad$ Acceleration, $a=\frac{F}{m}$ $=\frac{-8 \, N}{0.4\, kg}$ $=-20 \, m \,s^{-2}$
The position of the body at any time t is given by
$x=x_{0}$ $+u t$ $+\frac{1}{2} \,a t^{2}$
The position of the body at $t = 0$ is $0,$ therefore $x_{0}=0.$
$\therefore\quad$ $x=u t$ $+\frac{1}{2} a t^{2}$
Position of the body at $t = 25 \,s$
Here, $u=10 \, m \, s^{-1},$ $a=-20 \,m \,s^{-2},$ $t=25\, s$
$\therefore\quad$ $x=10\times25$ $+\frac{1}{2}$ $\left(-20\right)$ $\left(25\right)^{2}$ $=250$ $-6250$ $=-6000 \,m$