Question

How long will it take for a car to come to a complete stop when traveling at 45 miles per hour if its acceleration is -3 miles/hr/sec?

Answer 1

15 sec

Explanation:

Given:

Initial speed (u) = 45 mph

Final speed (v) = 0 mph

Acceleration (a) = -3 mph/s

To make it easier to calculate them, we convert all units to the same unit, distance in meters and time in seconds, therefore:

`\begin{gathered} \text{ 1 Miles per hour \lbrack mph\rbrack equals 0.44704 Meters per second \lbrack m/s\rbrack} \\ \\ \text{ 1 Mile per hour per second \lbrack mph/s\rbrack equals 0.44704 Meters per second}^2\text{ \lbrack m/s}^2\text{\rbrack} \\ \\ \text{ Therefore:} \\ \\ u=45\text{ mph}\cdot\frac{0.44704\text{ m/s}}{1\text{ mph}}=20.1168\text{ m/s} \\ \\ a=-3\text{ mph/s}\cdot\frac{0.44704\text{ m/s}^2}{1\text{ mph/s}}=-1.34112\text{ m/s}^2 \end{gathered}`

Now, we use the following formula to calculate the braking time:

`\begin{gathered} v=ut+at^2 \\ \\ \text{ we replacing} \\ \\ 0=20.1168\cdot t+(-1.34112)t^2 \\ \\ 0=t(20.1168-1.34112t) \\ \\ 20.1168-1.34112t=0 \\ \\ t=(20.1168)/(1.34112) \\ \\ t=\text{ 15 ec} \end{gathered}`

That is, it will take 15 seconds to stop.