Question

A car going at 80 mph comes to a complete stop in 6 seconds. Calculate the acceleration

Answer 1

The acceleration is defined as:

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

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:

`80(mi)/(h)\cdot\frac{5280\text{ ft}}{1\text{ mi}}\cdot\frac{1\text{ h}}{3600\text{ s}}=117.33(ft)/(s)`

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:

`\begin{gathered} a=(0-117.33)/(6) \\ a=-19.56 \end{gathered}`

Therefore, the acceleration is -19.56 feet per second per second. Note: The minus sign indicates that the car is slowing down.