MOTION Speed, distance, time, velocity, and acceleration

What is motion? Motion is a change in an object’s position. When something moves, it is in motion. A motionless object is at rest, or stationary.

To understand how to describe motion, think about the movement of a bicycle. To describe how fast the bicycle is traveling, you have to know two things about its motion. One is the distance it has traveled, or how far it has gone. The other is how much time it took to travel that distance. To find the biker’s average speed, divide the distance down the hill by the time taken to cover that distance. What would happen to the average speed if the hill were steeper?

Average Speed Is calculated by dividing the distance traveled by the amount of time it takes to travel that distance Can be calculated by the following equation: Average speed = total distance traveled OR S = d travel time t Because average speed is calculated by dividing distance by time, its units always will be a distance unit divided by a time unit. EXAMPLE: mi/hr or ft/sec

Calculating Average Speed Riding your bike, it takes you 30 min to get to your friend’s house, which is 9 mi away. What is your average speed? 1. This is what you know: distance: d = 9 mi time = 30 min = 0.5 h 2. This is what you need to know: speed: s 3. This is the equation you need to use: s = d/t 4. Substitute the known values: s = 9 mi/0.5 h = ??? ANSWER: 18 mi/h

Average speed is useful if you don’t care about the details of the motion. For example, suppose you went on a long road trip and traveled 640 miles in 8 hours. Your average speed was 80 mi/h, even though you might have stopped for red lights, got stuck in a traffic jam, or enjoyed a long stretch of high speed on a highway.

Instantaneous Speed Is the speed of an object at any instant in time When you ride in a car, the instantaneous speed is given by the speedometer. How does the instantaneous speed of the skater change as he travels down the half pipe?

Constant Speed Happens when the instantaneous speed does not change EXAMPLE: a car driving on cruise control When a car is traveling at a constant speed, its average speed and its instantaneous speed are the same.

Total distance traveled = average speed X time If an object is moving with constant speed, then the distance it travels over any period of time can be calculated using the equation for average speed. Can be calculated using the following equation: Total distance traveled = average speed X time OR d = s X t

Calculating Distance It takes your family 2 h to drive to an amusement park at an average speed of 73 mi/h. How far away is the amusement park? 1. This is what you know: speed: s = 73 mi/h time: t = 2 h 2. This is what you need to know: distance: d 3. This is the equation you need to use: d = s X t 4. Substitute the known values: d = 73 mi/h X 2 h = ??? ANSWER: 146 mi

Velocity Is the speed of an object and its direction of motion Changes when speed changes, the direction of motion changes, or both change If a car is traveling straight at a constant speed and then turns right, continuing at the same speed, the car’s velocity has changed. What is another way the car could change its velocity?

Acceleration Is the change in velocity divided by the time needed for that change to happen If the velocity of an object is changing, the object has acceleration. The direction of the acceleration depends on whether the object is speeding up or slowing down. If an object it traveling on a level surface with a constant velocity, its acceleration is zero.

Acceleration OR a = (final speed – initial speed) If the direction of motion isn’t changing, then the acceleration can be calculated from the following formula: Acceleration = change in speed time OR a = (final speed – initial speed) Initial speed is the speed at the beginning of the time period. Final speed is the speed at the end of the time period.

Calculating Acceleration You are sliding on a snow covered hill at a speed of 8 ft/s. There is a drop that increases your speed to 18 ft/s in 5 s. Find your acceleration. 1. This is what you know: initial speed: = 8 ft/s final speed: = 18 ft/s time: t = 5 s 2. This is what you need to know: acceleration: a 3. This is the equation you need to use: a = (final speed – initial speed) time 4. Substitute the known values: a = (18 ft/s – 8 ft/s) ÷ 5 s a = 10 ft/s ÷ 5 s = ??? ANSWER: 2 ft/s²