We are given that a car decelerates from 29 m/s to 15.8 m/s in 6.37 seconds. To determine the force that causes de deceleration we will use Newton's second law:
[tex]F=ma[/tex]Where:
[tex]\begin{gathered} F=\text{ force} \\ m=\text{ mass} \\ a=\text{ acceleration} \end{gathered}[/tex]We are given the mass therefore we need to determine the acceleration. To do that we will use the following equation of motion:
[tex]v_f=v_0+at_{}[/tex]Where:
[tex]\begin{gathered} v_f,v_0=\text{ final and initial velocities} \\ a=\text{ acceleration} \\ t=\text{ time} \end{gathered}[/tex]Now, we solve for the acceleration. First, by subtracting the initial velocity from both sides:
[tex]v_f-v_0=at[/tex]Now, we divide both sides by "t":
[tex]\frac{v_f-v_0}{t}=a[/tex]Now, we plug in the given values of velocity and time:
[tex]\frac{15.5\frac{m}{s}-29\frac{m}{s}}{6.37s}=a[/tex]Solving the operations:
[tex]-2.12\frac{m}{s^2}=a[/tex]Now, we use this value together with the mass to determine the force:
[tex]F=(1370\operatorname{kg})(-2.12\frac{m}{s^2})[/tex]Solving the product:
[tex]F=-2903.45N[/tex]Therefore, the magnitude of the force is 2903.45 Newtons.
