Question

A car traveling at 10.2 meters per second crashes into a barrier and stops in 0.330 meters. What force must be exerted on a child of mass 28.3 kilograms to stop him or her in the same time as the car? Answer must be in 3 significant digits. Include units.

Answer 1

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

`\begin{gathered} v^2=u^2+2as \\ a=(v^2-u^2)/(2s) \end{gathered}`

Substitute the known values in the above expression as

`\begin{gathered} a=((0)^2-(10.2)^2)/(2(0.330)) \\ =-157.63m/s^2 \end{gathered}`

The magnitude of the force must be exerted on a child is calculated as

`\begin{gathered} F=ma \\ =(28.3)(157.63) \\ =4460.92\text{ N} \end{gathered}`

Hence, the force must be exerted on a child is F = 4460.92 N