Speed & Velocity

State Performance Indicator SPI – Apply proper equations to solve basic problems pertaining to distance, time, speed, and velocity. Prior Knowledge What do we know about: Distance? Time? Speed? Velocity?

What is Speed? Speed is the distance traveled by an object divided by the time it took to travel that distance. Scientists calculate speed using the following equation:

Measuring Speed in Units Speed only gives distance and time. Examples of distance in relation to time: m/s km/s m/h km/h These units of measurement are read, “meters PER second, kilometers PER hour…” Never write MPS!

Speed Do you always walk at the same pace? Do your parents always drive right at the speed limit? Most objects do not travel at a constant speed. So, it is very useful to calculate the average speed of objects instead.

How to calculate average speed To calculate the average speed at which an object travels… …divide the total distance of the trip by the total time of travel.

Practice 1. Mr. Evans lives about 30 miles away from Tyner Academy. If it took him 1 hour to drive to school today, what was his average speed? Total distance (d) = Total time (t) = Average speed (s) = ? = 30 miles/hour 30 miles/hour 30 miles 1 hour

2. A baseball is thrown and travels 11 meters in 1 second. Calculate the average speed of the ball. Total distance (d) = 11 meters Total time (t) = 1 second Average speed (s) = ? 11 m/s

Consider… Two birds leave the same tree at the exact same time. Both birds begin flying at a speed of 10 km/h for 5 min, then increase to 12 km/h for 8 min, and slow down to 5 km/h for 10 min before resting. If their speeds were identical, how did the birds end up in two different locations? Answer: Our birds shared the same speed, but they had different velocities.

Velocity: Direction Matters Velocity is the speed of an object in a particular direction. Examples of velocities: An airplane flying 600 km/h south A car traveling 70 mi/h northeast Be careful NOT to confuse speed with velocity.

Velocity (v) describes the motion AND direction an object travels in. If either the speed or direction of an object changes, the velocity changes also. The formula for velocity is very similar to the formula for average speed:

Follow the steps to solve the equation: Distance (d) = 5 meters Time (t) = 3 seconds Velocity (v) = ? Write down known facts Write the formula you will use to solve. Plug in the numbers for known variables. Do the math. v = meters/second Your velocity is about 1.7 meters per second. You walk 5 meters for 3 seconds. What is your velocity?

Thinking further Sound travels at a speed of 330 m/s. If a lightening bolt strikes the ground 1km away from you, how long will it take for the sound to reach you? What’s different about this problem? How do we solve if the variable for time is not given? What do we do if the variable for distance is not given?

Speed & Velocity Equations: The Magic Triangle d v t Speed (s) and velocity (v) can be interchanged, if necessary.

Sample Problem Problem: 2. Sound travels at a speed of 330 m/s. If a lightening bolt strikes the ground 1km away from you, how long will it take for the sound to reach you? Step 1: Write what you know. Step 2: Write the formula. Step 3: Plug in the numbers. x 1000 * 1 km = 1000m Step 4: SolveSolution: s = 330 m/s d = 1 km t = ? It will take 3.03 seconds 3.03 seconds for the sound to reach you.

Calculating Average Speed & Velocity Use the formulas we have discussed to answer the following practice problems. 2. A car travels a distance of 16 meters in 1.8 seconds. What speed is the car traveling at? Step 1: Write what you know. Step 2: Write the formula. Step 3: Plug in the numbers. Step 4: Solve. d = 16 m t = 1.8 s v = ?

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?

Practice Problems 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 2,541 meters through the park and the time it took to cover that distance was 43.6 minutes, what was the speed of the jogger?

Practice Problems 7. Which object has a greater velocity, a ball rolling down a 3.4 meter hill in 6 seconds or a fish swimming upstream and covering 5.4 meters in 0.4 minutes? 8. If a man decides to walk across town to a store that is.95 kilometers away, and he has only 25 minutes to get there, what speed does he need to maintain to arrive on time? 9. If a projectile flies north 387 meters in 5.8 seconds, what is its velocity?

Practice Problems 10. Calculate the velocity of a mountain climber if he or she is moving northeast at a pace of 1.6 km in 1.4 hours. Give your answer in the SI unit for velocity.