Equation... Gives you... If you know... v = d/t speed distance and time. t = d/v time distance and speed
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1 Name: Date: Velocity and Speed Speed To determine the speed of an object, you need to know the distance traveled and the time taken to travel that distance. However, by rearranging the formula for speed, v = d/t, you can also determine the distance traveled or the time it took for the object to travel that distance, if you know the speed. For example, Equation... Gives you... If you know... v = d/t speed distance and time d = v t distance speed and time t = d/v time distance and speed Use the SI system to solve the practice problems unless you are asked to write the answer using the English system of measurement. As you solve the problems, include all units and cancel appropriately. Example 1: What is the speed of a cheetah that travels meters in 4.0 seconds? Speed of the cheetah. Distance = meters Time = 4.0 seconds The speed of the cheetah is 28 meters per second. Example 2: There are 1,609 meters in one mile. What is this cheetah s speed in miles/hour? Speed of the cheetah in miles per hour. Distance = meters Time = 4.0 seconds The speed of the cheetah in miles per hour is 63 mph. s and 1, 609 meters = 1 mile
2 YOUR TURN! 1. A bicyclist travels 60.0 kilometers in 3.5 hours. What is the cyclist s average speed? s 2. What is the average speed of a car that traveled miles in 5.5 hours? s 3. How much time would it take for the sound of thunder to travel 1,500 meters if sound travels at a speed of 330 m/s? s 4. How much time would it take for an airplane to reach its destination if it traveled at an average speed of 790 kilometers/hour for a distance of 4,700 kilometers? What is the airplane s speed in miles/ hour? s
3 Velocity: Speed and velocity do not have the same meaning to scientists. Speed is a scalar quantity, which means it can be completely described by its magnitude (or size). The magnitude is given by a number and a unit. For example, an object s speed may be measured as 15 meters per second. Velocity is a vector quantity. In order to measure a vector quantity, you must know the both its magnitude and direction. The velocity of an object is determined by measuring both the speed and direction in which an object is traveling. If the speed of an object changes, then its velocity also changes. If the direction in which an object is traveling changes, then its velocity changes. A change in either speed, direction, or both causes a change in velocity. You can use v = d/t to solve velocity problems in the same manner that you changed the form of the equation to solve speed problems in Part A. The boldfaced v is used to represent velocity as a vector quantity. The variables d and t are used for distance and time. The velocity of an object in motion is equal to the distance it travels per unit of time in a given direction. Example 1: What is the velocity of a car that travels meters, northeast in 4.65 seconds? Velocity of the car. Distance = meters The velocity of the car is 21.5 meters per second, northeast. Time = 4.65 seconds Example 2: A boat travels with a velocity equal to 14.0 meters per second, east in 5.15 seconds. What distance in meters does the boat travel? Distance the boat travels. Velocity = 14.0 meters per second, east The boat travels 72.1 meters. Time = 5.15 seconds
4 YOUR TURN! 5. An airplane flies 525 kilometers north in 1.25 hours. What is the airplane s velocity? 6. A soccer player kicks a ball 6.5 meters. How much time is needed for the ball to travel this distance if its velocity is 22 meters per second, south? 7. A cruise ship travels east across a river at 19.0 meters per minute. If the river is 4,250 meters wide, how long does it take for the ship to reach the other side?
5 MIXED SPEED AND VELOCITY PROBLEMS 8. How far can a person run in 15 minutes if he or she runs at an average speed of 16 km/hr? (HINT: Remember to convert minutes to hours.) 9. A bus is traveling at 79.7 kilometers per hour east, how far does the bus travel 1.45 hours? 10. A shopping cart is pushed 15.6 meters west across a parking lot in 5.2 seconds. What is the velocity of the shopping cart?
6 11. A volcanologist noted that lava rushed down a mountain at 32.2 kilometers per hour, south. How far did the lava flow in 17.5 minutes? 12. A snail can move approximately 0.30 meters per minute. How many meters can the snail cover in 15 minutes? 13. A driver realizes that she is traveling in the wrong direction on a one-way street. She has already driven 3.5 meters at a velocity of 16 meters per second, east before deciding to make a U-turn. How long did it take for the driver to realize her error?
7 14. A person in a kayak paddles down river at an average speed of 10 km/h. After 3.25 hours, how far has she traveled? 15. The same person in question 18 paddles upstream at an average speed of 4 km/h. How long would it take her to get back to her starting point? 16. A family drives 881 miles from Houston, Texas to Santa Fe, New Mexico for vacation. How long will it take the family to reach their destination if they travel at a velocity of 55.0 miles per hour, northwest?
8 17. Juan s mother drives 12.5 miles southwest to her favorite shopping mall. What is the velocity of her automobile if she arrives at the mall in 7.25 minutes? 18. A train travels 225 kilometers in 2.5 hours. What is the train s average speed? 19. How far will you travel if you run for 10 minutes at 2 m/s?
t 4.0 sec. 2. A bicyclist travels 60.0 kilometers in 3.5 hours. What is the cyclist s average speed?
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