Speed, distance and time simulator

What this simulator shows

Speed tells you how far something travels in each unit of time. Set each car's speed from 1 to 10 meters per second, give the blue car a head start if you like, choose who you think will win, and press Go. The cars race in real time along a 100 m track, and a distance–time graph draws both journeys live. The readout shows each car's distance and time, and divides one by the other. Races stop after 20 seconds, so very slow cars may not finish.

• Speed = distance ÷ time. A car that goes 40 m in 5 s has a speed of 8 m/s.
• Time = distance ÷ speed. At 8 m/s, 100 m takes 12.5 s.
• On a distance–time graph, a steeper line means a faster speed. A flat line means stopped.
• A head start moves a line up the distance axis without changing its slope.

Why a live graph helps

Distance–time graphs can feel abstract on paper. Watching a line grow while the car moves links each point to a moment in the race: this high, at this time. Students quickly see that the faster car's line is steeper, and that a car with a head start begins higher up, which prepares them for slope and starting values in algebra.

Common misconceptions

A common mistake is reading a distance–time graph as a picture of the track or a hill, so a steep line looks like going uphill. It means going fast. Another is mixing up the formula and multiplying distance by time. Checking the units helps: meters divided by seconds gives meters per second. Students also tend to assume the faster car always wins. With a head start, a slower car can finish first, and the tie challenge makes students reason with the formula rather than guess.

For a sense of scale, 10 m/s is about 22 miles per hour, roughly the top speed of the world's fastest sprinters.

A 10-minute speed activity

• Set red to 10 m/s and blue to 5 m/s with no head start. Ask the child to predict both finish times, then race.
• Pause a race at about 6 s. Ask them to work out each car's speed from the readout's distance and time.
• Give blue a 50 m head start. Ask: "What speed does blue need to tie with red at 10 m/s?"
• Race to check (5 m/s). Look at the graph: where do the lines meet?
• Ask them to describe in words what a steeper line means.

Where this fits in school

• US, grade 6: Common Core 6.RP.A.3b covers unit rate problems, including constant speed.
• US, grade 7: Common Core 7.RP.A.2 asks students to recognize and represent proportional relationships. With no head start, distance is proportional to time; with one, it is not.
• England, Key Stage 3: pupils learn that average speed = distance ÷ time and represent a journey on a distance–time graph; maths lessons also cover compound units such as speed.

Learning more

Rates and graphs appear on Eurekami's skill map in both math and science. Lessons work through problems like these step by step, and daily practice keeps the speed formula fresh with a few quick questions.