Given data
*The given initial speed of the car is u = 10.2 m/s
*The given final speed of the car is v = 0 m/s
*The given distance is s = 0.330 m
*The given mass of the child is m = 28.3 kg
The formula for the acceleration of the child is given by the equation of motion as
[tex]\begin{gathered} v^2=u^2+2as \\ a=\frac{v^2-u^2}{2s} \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} a=\frac{(0)^2-(10.2)^2}{2(0.330)} \\ =-157.63m/s^2 \end{gathered}[/tex]The magnitude of the force must be exerted on a child is calculated as
[tex]\begin{gathered} F=ma \\ =(28.3)(157.63) \\ =4460.92\text{ N} \end{gathered}[/tex]Hence, the force must be exerted on a child is F = 4460.92 N
