Question

A body of mass $0.4 \,kg$ starting at origin at $t = 0$ with a speed of $10 \,m\,s^{-1}$ 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)

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