The acceleration is defined as:
[tex]a=\frac{v_f-v_0}{t}[/tex]where vf is the final velocity, v0 is the initial velocity and t is the time. In this case we have:
The initial velocity is 80 mph
The final velocity is 0 mph (since the car stops)
The time it takes to slow down is 6 seconds.
Before we can do the calculation, we need to convert the velocity to appropriate units; let's write the initial velocity in ft/s units. To do this we need to remember that 1 mile is equal to 5280 ft and one hour is equal to 3600 s, then we have:
[tex]80\frac{mi}{h}\cdot\frac{5280\text{ ft}}{1\text{ mi}}\cdot\frac{1\text{ h}}{3600\text{ s}}=117.33\frac{ft}{s}[/tex]Hence the initial velocity is 177.33 ft/s.
Now that we have all the values we need, we plug them in the equation for the acceleration:
[tex]\begin{gathered} a=\frac{0-117.33}{6} \\ a=-19.56 \end{gathered}[/tex]Therefore, the acceleration is -19.56 feet per second per second. Note: The minus sign indicates that the car is slowing down.
