We are given the following information
Mass = m = 45.0 kg
Initial speed = vi = 40.0 m/s
Time = t = 0.500 s
We are asked to find the average force that the seat belt exerted on her.
Recall from Newton's second law of motion,
[tex]F=m\cdot a[/tex]Where a is the acceleration of the car and is given by
[tex]v_f=v_i+a\cdot t[/tex]Where vf is the final velocity of the car that must be 0 since the car was stopped.
[tex]\begin{gathered} 0=40.0+a\cdot0.500 \\ a=\frac{-40.0}{0.500} \\ a=-80\; \; \frac{m}{s^2} \end{gathered}[/tex]The negative sign indicates deacceleration since the card was stopped.
So, the force is
[tex]\begin{gathered} F=m\cdot a \\ F=45\cdot80 \\ F=3600\; N \end{gathered}[/tex]Therefore, the seat belt exerted a force of 3600 N on her.
