Respuesta :
First, determine the acceleration of the motion of the car, by using the following formula:
[tex]v^2=v^2_0+2ax[/tex]where,
v: final velocity = 0m/s
vo: initial mvelocity = 10.2 m/s
a: acceleration = ?
x: distance = 0.330 m
Solve the equation above for a and replace the previous values of the parameters:
[tex]a=\frac{v^2-v^2_o}{2x}=\frac{(0\frac{m}{s})^2-(10.2\frac{m}{s})^2}{2(0.330m)}=-157.636\frac{m}{s^2}[/tex]minus sign means that there is a deceleration,
Now, use the Newton second law by using the previous result. Consider that time needed to stop a child with the given mass is the same time obtained with the previous acceleration in case the child moves with the same velocity as the car. Then:
[tex]F=m\cdot a[/tex]where m = 28.3 kg (mass of the child) and a is the previous result we got. Replace these values to obtain the required force.
[tex]F=(28.3kg)(157.636\frac{m}{s^2})=4461.109N[/tex]with three significant digits you have:
F = 4461 N
