Chemistry · General chemistry I · Worked example

Convert a speed from mi/h to m/s

A car travels at $65.0$ miles per hour. What is its speed in meters per second? Use $1 mi = 1.6093 km$ .

Plan both units

A speed has two units. Miles on top must become meters, and hours on the bottom must become seconds. Each needs its own factors, and they can all go in one chain.

Convert the distance

Miles to kilometers, then kilometers to meters. $1 mi = 1.6093 km$ is a rounded form of the defined $1.609344 km$ , with five figures, more than the three of $65.0$ . $1 km = 1000 m$ is exact.

65.0 \frac{mi}{h} \times \frac{1.6093 km}{1 mi} \times \frac{1000 m}{1 km}

\begin{array}{c} 65.0 \frac{mi}{h} \times \frac{1.6093 km}{1 mi} \\ \times \frac{1000 m}{1 km} \end{array}

Convert the time

The hours sit on the bottom of $mi / h$ . To cancel them, the factor must have hours on top, $1 h$ over $3600 s$ . This is the step most often flipped, because the usual instinct is to put the bigger number on top.

\times \frac{1 h}{3600 s}

Multiply and round

$65.0 \times 1.6093 \times 1000 \div 3600$ $= 29.0568$ . Only $65.0$ limits the precision, so the speed is $29.1 m / s$ .

65.0 \frac{mi}{h} \times \frac{1.6093 km}{1 mi} \times \frac{1000 m}{1 km} \times \frac{1 h}{3600 s} = 29.1 \frac{m}{s}

\begin{array}{c} 65.0 \frac{mi}{h} \times \frac{1.6093 km}{1 mi} \\ \times \frac{1000 m}{1 km} \times \frac{1 h}{3600 s} \\ = 29.1 \frac{m}{s} \end{array}

Check the size

A mile is about $1600 m$ and an hour is $3600 s$ , so $1 mi / h$ is a little under half a meter per second, about $0.45 m / s$ . $65 \times 0.45 \approx 29$ , which matches. With the time factor flipped, the number would come out near $3.8 \times 10^{8}$ , faster than any car.

Result

$65.0 mi / h$ is $29.1 m / s$ .

Your turn

1. One like the example

A cyclist on a long descent reaches $25.0 m / s$ . What is that speed in kilometers per hour?

Show the answer and explanation

$90.0 km / h$ .

Meters on top become kilometers with $1 km$ over $1000 m$ . Seconds on the bottom become hours with $3600 s$ over $1 h$ , which puts seconds on top to cancel. $25.0 \times 3600 \div 1000$ $= 90.0 km / h$ .

\begin{array}{l} v = 25.0 m/s \\ 25.0 m/s \times \frac{1 km}{1000 m} \times \frac{3600 s}{1 h} = 90.0 km/h \end{array}

\begin{array}{c} v = 25.0 m/s \\ 25.0 m/s \times \frac{1 km}{1000 m} \\ \times \frac{3600 s}{1 h} = 90.0 km/h \end{array}

2. A variation

A pump delivers $2.50 L / \min$ . What is that in milliliters per second?

Show the answer and explanation

$41.7 mL / s$ .

Liters on top become milliliters with $1000 mL$ over $1 L$ . Minutes on the bottom become seconds with $1 \min$ over $60 s$ . $2.50 \times 1000 \div 60 = 41.67$ , which is $41.7 mL / s$ to three figures.

\begin{array}{l} Q = 2.50 L/min \\ 2.50 L/min \times \frac{1000 mL}{1 L} \times \frac{1 \min}{60 s} = 41.7 mL/s \end{array}

\begin{array}{c} Q = 2.50 L/min \\ 2.50 L/min \times \frac{1000 mL}{1 L} \\ \times \frac{1 \min}{60 s} = 41.7 mL/s \end{array}

3. Somewhere new

A tank is a cube $2.00 m$ on each edge. How many liters does it hold?

Show the answer and explanation

$8.00 \times 10^{3} L$ .

The volume is ${(2.00 m)}^{3} = 8.00 m^{3}$ . A cubic meter is exactly $1000 L$ , because it is ${(10 dm)}^{3}$ and a cubic decimeter is a liter. $8.00 m^{3} \times 1000 L / 1 m^{3}$ $= 8.00 \times 10^{3} L$ . Using $1 m = 10 dm$ without cubing it would give $80 L$ , a thousand times too little.

\begin{array}{l} a = 2.00 m \\ V = a^{3} \\ V = {(2.00 m)}^{3} = 8.00 m^{3} \\ 8.00 m^{3} \times \frac{1000 L}{1 m^{3}} = 8.00 \times 10^{3} L \end{array}

\begin{array}{c} a = 2.00 m \\ V = a^{3} \\ V = {(2.00 m)}^{3} = 8.00 m^{3} \\ 8.00 m^{3} \times \frac{1000 L}{1 m^{3}} \\ = 8.00 \times 10^{3} L \end{array}

Keep exploring

Open the chain in a Chemistry box and change $65.0 mi / h$ to $55.0 mi / h$ . The row reads ✗ until you write the new speed, $24.6 m / s$ .

Return to the concept →

Sources and scope

Authored study material. Tool results depend on the stated inputs and model assumptions.

After reading

Study it, then try it

Practice the key terms as flashcards, then open the example in its tool, change a value and keep a useful result on your board.

Study the 6 key terms Check the speed in a Chemistry box Open worked example on a board Conversion factors

Your existing work stays on this device. Examples open as editable copies.

Plan both units

Convert the distance

Convert the time

Multiply and round

Check the size

Result

Your turn

1. One like the example

90.0 km⁢/⁢h90.0 km/h.

2. A variation

41.7 mL⁢/⁢s41.7 mL/s.

3. Somewhere new

8.00×103 L8.00×103 L.

Keep exploring

Study it, then try it

$90.0 km / h$ .

$41.7 mL / s$ .

$8.00 \times 10^{3} L$ .