Expert: Daniel Mazur - 6/5/2007

Question
Hello Daniel, We have read in physics, Speed = Distance / Time. So Speed is directly proportional to Distance. So if the speed increases Distance also increases?? Is this the meaning of the formula we have derived. The Distance cannot increase as the Speed increases. for eg, If we travel in a car at say 50 miles/hr for a distance of 100 kms, if we again travel at 80miles/hr, the Distance doesn't increase, its fixed!! Please explain the relation between these two components. Thanks in advance for your answers

Answer
Hello Mohan,

thank you for your question. It is true that Speed is defined as "Distance traveled" divided by "Time of travel". Let me assign symbols: Speed=V, Distance=D, Time=T. Then the definition states V=D/T, but depending on your problem you can equivalently write this as D=V*T or T=D/V. In every situation you need to pick the form that is useful at the moment.

Solution to your Example: If we travel distance D=100 km with average speed V=50 km/h, the *unknown variable* is Time, T=D/V=100/50=2 h. If we travel the same Distance at an increased speed V=80km/h then of course Distance remains the same, simply because we made it so. What changes is the Time of travel, which shortens according to the same equation T=D/V=100/80=1.25 h (1 hour 15 minutes).

The key to understand these things is to recognize that an equation can be written in several equivalent ways and that with every problem you pick the most suitable one. Let me give you another, a little more advanced example along with its solution.

Another Example: You ride your bike to school one day, it takes you 15 minutes (0.25 hour) and the speedometer tells you that your average speed was 10 km/h. The next day you walk the same distance to school instead and it takes you 45 minutes (0.75 hour). Can you tell from this, what was the speed of your walk?

Solution: In this problem you will use the form of your equation D=V*T. The distance is not known, but that doesn't stop us! We have a pair of Velocity and Time for bike ride, let's use symbols V1=10 km/h, T1=0.25 h, and then we have a pair of Velocity and Time for walking, V2 is unknown and T2=0.75 h.

The trick is to recognize that the distance D was the same for both bike and walk. For bike we know that D=V1*T1 and for walk we know D=V2*T2. Now because the D's are the same, these two equations can be put together as (D=) V1*T1=V2*T2. In this last equation V1*T1=V2*T2 there are 3 known numbers and 1 unknown, which is the V2, the speed of walking that we are looking for. We can transform the equation into another, equivalent form V2=V1*T1/T2, which leaves everything unknown on the left and all known on the right. So, V2=10*0.25/0.75=3.3 km/h. And this is the answer, this is the speed of the walk.

I recommend that you read this carefully, take breaks as much as you like, and do *not* panic! You will get comfortable with it through practice and solving a number of these problems with a tutor and by yourself.

Good luck!
Daniel