Question

A 1370-kg car is moving due east with an initial speed of 29.0 m/s. After 6.37 s the car has slowed down to 15.8 m/s. Find the magnitude of the net force that produces the deceleration.Number________ Units________

Answer 1

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:

`F=ma`

Where:

`\begin{gathered} F=\text{ force} \\ m=\text{ mass} \\ a=\text{ acceleration} \end{gathered}`

We are given the mass therefore we need to determine the acceleration. To do that we will use the following equation of motion:

`v_f=v_0+at_{}`

Where:

`\begin{gathered} v_f,v_0=\text{ final and initial velocities} \\ a=\text{ acceleration} \\ t=\text{ time} \end{gathered}`

Now, we solve for the acceleration. First, by subtracting the initial velocity from both sides:

`v_f-v_0=at`

Now, we divide both sides by "t":

`(v_f-v_0)/(t)=a`

Now, we plug in the given values of velocity and time:

`(15.5(m)/(s)-29(m)/(s))/(6.37s)=a`

Solving the operations:

`-2.12(m)/(s^2)=a`

Now, we use this value together with the mass to determine the force:

Solving the product:

`F=-2903.45N`

Therefore, the magnitude of the force is 2903.45 Newtons.