## MATH - SCIENCE INTEGRATION

### Calculating Speed and Velocity

 The trouble with facts is that there are so many of them. {HYPERLINK "/quotes/Samuel_McChord_Crothers/"} Samuel McChord Crothers , The Gentle Reader

### Methods for calculating

 Whenever we work on solving any motion problems we will be working with an equation that requires a step-by-step method.

 Careful attention needs to be paid to writing out the known and unknown measurements, the SI units involved, and the entering of numbers into your calculator. Double check all work!

 No need to ask the question "Do we have to show all of our work?" The unqualified answer to that question is YES !   Numbers mean nothing in measurements and science calculations if they are not labeled with some type of unit.   Physics problems mean nothing without proof of your answer and that comes with writing out the equation.   So let's get to it!

• Procedure for Solving
 SPEED and VELOCITY EQUATION:   speed = distance          OR        v =  d                  time                                t

 Remember that the SI unit for speed and velocity is meters per second (m/s).  Velocity answers also require a direction. The best way to learn the steps is to work through a problem. If you need to review solving one step equations, click on the link below.

• Speed of a Sailboat
 Problem :  What is the speed of a sailboat that is traveling 100 meters in 120 seconds?

 Step 1 :  Write down the equation you need to solve the problem. v =  d           t

 Step 2 :  Place the known information into the equation. Known :  The sailboat traveled a distance of 100 meters and the time it took to travel that distance was 120 seconds.  Since meters per second is the SI unit for speed, there is no need for conversions in this problem. v =  100m  =        120 s

 Step 3 : Solve.  Carefully enter the numbers into your calculator. Remember that this is a division problem. Check to make sure that your solution contains the correct SI unit. SOLUTION : The sailboat has a speed of .83m/s.

 One more example problem and then you will practice on your own.

• Speed of a Cyclist
 Problem :  If a cyclist in the Tour de France traveled southwest a distance of 12,250 meters in one hour, what would the velocity of the cyclist be?

 Remember that the SI unit for velocity is meters per second, but this problem has the distance measure in meters and the time measured in hours.  The 1 hour has to be converted to seconds.  If you need to review conversions, click here.  Also, this is a velocity problem and your solution requires a direction.

 Step 1 : Write down the equation needed for the problem. v= d       t

 Step 2 :  Enter all the known values into the equation, taking care to make all necessary conversions. v = 12,250 m =         3,200s

 Step 3 : Use your calculator to solve the problem. Check to make sure that you included the correct SI unit and direction. SOLUTION :   3.83 m/s southwest

• Speed and Velocity Practice Problems
 PRACTICE PROBLEMS : 1.   Calculate the speed of a dog running through a field if he is covering 23.7 meters in 54 seconds. 2.   If a cross country runner covers a distance of 347 meters in 134 seconds what is her speed? 3.   What is the speed of a baseball that travels 49 meters in 2.4 seconds? 4.   What is the speed of a horse in meters per second that runs a distance of 1.2 miles in 2.4 minutes?   5.   Calculate the velocity of a car that travels 556 kilometers northeast in 3.4 hours.  Leave your answer in kilometers per hour. 6.   If the distance covered by a jogger is 2,541meters through the park and the time it took to cover that distance was 43.6 minutes, what was the speed of the jogger? 7.   Which object has a greater velocity, a ball rolling down a 3.4 meter hill in six seconds or a fish swimming upstream and covering 5.4 meters in 0.4 minutes? 8.   If Seneca decides to walk across town to a store that is .95 kilometers away and she has only 25 minutes to get there, what speed does she need to maintain to arrive on time? 9.   If a projectile flies north 387 meters in 5.8 seconds, what is its velocity? 10.   Calculate the velocity of a mountain climber if that climber is moving northeast at a pace of 1.6 km in 1.4 hours?  Give your answer in the SI unit for velocity.