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A 1,066 kg car moving at 86.55 km/h comes to a stop in 4.163 s.The magnitude of the net force on the can in Newtons is:

Sagot :

First, we find the acceleration of the car using the following formula.

[tex]v_f=v_0+at[/tex]

Where the final speed is zero (because the car stops), the initial speed is 86.55 km/h, and the time is 4.163 seconds. Let's replace these magnitudes and solve for a.

[tex]\begin{gathered} 0=86.55(\frac{km}{h})+a\cdot4.163\sec \\ -86.55(\frac{km}{h})=a\cdot4.163\sec \\ a=\frac{-86.55(\frac{km}{h})}{4.163\sec } \end{gathered}[/tex]

But, we have to transform the speed from km/h to m/s.

[tex]\frac{86.55\operatorname{km}}{h}\cdot\frac{1000m}{1\operatorname{km}}\cdot\frac{1h}{3600\sec }\approx24.04(\frac{m}{s})[/tex]

Then, we use this transformation to find the acceleration.

[tex]\begin{gathered} a=\frac{-24.04(\frac{m}{s})}{4.163\sec } \\ a\approx5.77(\frac{m}{s^2}) \end{gathered}[/tex]

Once we have the acceleration, we can use Newton's Second Law to find the net force.

[tex]F=ma[/tex]

Let's replace the mass and acceleration to find F.

[tex]\begin{gathered} F=1066\operatorname{kg}\cdot5.77(\frac{m}{s^2}) \\ F=6150.82N \end{gathered}[/tex]

Therefore, the net force on the car is 6150.82 Newtons.