Question

The displacement of particle of mass 1 kg is given by the equation $x=t^3-2t^2-9$ where x in meter and t is sec. At $t=0$ , the force on the mass is

• A. 8 N
• B. 2 N
• C. -4 N
• D. -6 N

Answer 1

The correct option is C -4 N

As we know that acceleration is a second order derivative of displacement i.e., $a=\frac{d^{2}x}{d{t}^2}$
Since $x=t^3-2t^2-9$

$\Rightarrow \frac{dx}{dt}=3t^2-4t$

$\Rightarrow \frac{d^{2}x}{d{t}^2}=6t-4$
$\Rightarrow a=6t-4$
At $t=0$ sec, $a=-4m/s^2$
Since, Force $=$ mass $\times$ acceleration
$=m\times a$
$=1\times (-4)$
$=-4N$