Speed is the ratio between distance travelled as a function of time. It is used to describe the motion of an object.
Speed measurements are taken daily when travelling by car, bus, and by other modes of transportation. In these cases, speed is measured in kilometres per hour ( |\text{km/h}| ). However, the preferred unit of measurement in science is the metre per second ( |\text{m/s}| ).
The general equation used to calculate the speed is:
|v=\displaystyle \frac{\triangle x}{\triangle t}|
where
|v| stands for the speed |\text {(m/s)}|
|\triangle x| stands for the variation in position of the moving object |\left( x_{f} - x_{i} \right)| |\text {(m)}|
|\triangle t| stands for the variation of time |\left( t_{f} - t_{i} \right)| |\text {(s)}|
This formula is used to calculate the average speed or the instantaneous speed of an object at constant speed. For an object undergoing acceleration, a different type of motion must be taken into account, which is uniformly accelerated rectilinear motion (UARM).
What is the average speed of a car travelling at a distance of |\text {50 km}| in |\text {30 min}| ?
This data must first be transformed into the appropriate units for the speed formula, which is in metres and seconds.
|\text {50 km} \times 1000 = \text {50 000 m}|
|\text {30 min} \times \text {60 s/min} = \text {1800 s}|
The next step is to apply the speed formula.
||\begin{align} v=\displaystyle \frac{\triangle x}{\triangle t}\quad \Rightarrow \quad v &=\displaystyle \frac{\text {50 000 m}}{\text {1 800 s}} \\ &\cong \text {27.8 m/s}
\end{align}||
The car was travelling at an average speed of |\text {27.8 m/s}| .
To convert a speed in metres per second to kilometres per hour, the procedure is as follows:
|\displaystyle \frac{\text {m}}{\text {s}} \times \frac {\text {1 km}}{\text {1 000 m}} \times \frac {\text {3 600 s}}{\text {1 h}}|
More simply, just calculate:
|\displaystyle \frac{\text {m}}{\text {s}} \times 3.6 = \frac{\text {km}}{\text {h}}|
It is also possible to convert a speed from kilometres per hour into metres per second:
|\displaystyle \frac{\small \text {km}}{\text {h}} \times \frac {\text {1 000 m}}{\text {km}} \times \frac {\text {1 h}}{\text {3 600 s}}|
More simply, just calculate:
|\displaystyle \frac{\text {km}}{\text {h}} \div 3.6 = \frac{\text {m}}{\text {s}}|