Question

A person driving a car suddenly applies the brakes. The car takes four seconds to come to rest while traveling 20 m at constant acceleration.Can the speed of the car immediately before the brakes are applied be determined without first determining the car’s acceleration?a. Yes, by dividing the distance (20m) by the time (4s).b. Yes, by determining the average speed while braking and doubling it. c. No, because the acceleration is needed to use equations such as change in position=initial velocity + 1/2 acceleration • time^2d. No, because the fundamental relationship that defines velocity contains acceleration. Explain why choice A is wrong.Explain why the correct choice is correct. Use words like “average speed (or velocity)”, “initial speed (or velocity)”, “final speed (or velocity)”, “total distance”, and “total time.” Refer to appropriate basic motion equations.

Answer 1

ANSWER:

b. Yes, by determining the average speed while braking and doubling it.

STEP-BY-STEP EXPLANATION:

Option A is not correct because both speeds, the final and the initial, are not taken into account.

To determine the correct answer, the first thing to do is to do it mathematically. Just like this:

$\begin{gathered} v=u+at\rightarrow a=\frac{v-u}{t} \\ \\ s=ut+\frac{1}{2}at^2 \end{gathered}$

We replacing

$\begin{gathered} s=ut+\frac{1}{2}(\frac{v-u}{t})t^2 \\ \\ s=ut+\frac{1}{2}vt-\frac{1}{2}ut \\ \\ s=\frac{1}{2}t(u+v) \\ \\ v=0 \\ \\ s=\frac{1}{2}tu\rightarrow u=\frac{2s}{t} \end{gathered}$

The average speed, that is, the average between the initial speed and the final speed, is determined since the final speed is 0, because it ends up braking. We can calculate the initial start since we know the total braking time (4 seconds) and the total distance we also know to be 20 meters, using the previous equations.

Therefore, the correct answer is: b. Yes, by determining the average speed while braking and doubling it.