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Apply everything you have learned to analyze complex motion in sports and transportation.
How does a professional soccer player know exactly where to run to catch a 40-yard pass, or how does a self-driving car avoid a collision before a human even sees it?
To analyze motion like an engineer, we need three primary tools. Speed is simply how fast an object moves (a scalar). Velocity is speed with a specific direction (a vector). Finally, Acceleration is the rate at which velocity changes. In the real world, motion is rarely constant. A car pulling away from a stoplight is accelerating, while a car cruising on the highway at North has a constant velocity. If that car turns a corner—even without changing speed—its velocity changes because its direction changed. This means the car is technically accelerating! Understanding these differences allows us to map out the journey of any object, from a tennis ball to a rocket.
A sprinter runs a dash in heading East.
Quick Check
If a race car travels around a circular track at a perfectly steady 100 mph, is its velocity constant?
Answer
No, because its direction is constantly changing as it turns the track.
An electric scooter travels at a constant velocity of West. If the rider starts at a 'Position 0' and travels for , where will they be?
Quick Check
If you need to travel 20 kilometers and your bus moves at a constant 40 km/h, how long will the trip take?
Answer
0.5 hours (or 30 minutes), because .
Most real-world trips follow a three-part Motion Profile. 1. Acceleration Phase: The object speeds up from rest. 2. Cruise Phase: The object maintains a constant velocity. 3. Deceleration Phase: The object slows down to a stop (negative acceleration).
To analyze a full trip, we must calculate the distance covered in each phase separately. For example, a subway train spends a lot of time in phases 1 and 3 because the stations are close together. A cross-country airplane spends 90% of its time in the Cruise Phase. By breaking motion into these 'chunks,' we can calculate total fuel usage, travel time, and the forces acting on the passengers.
A delivery drone performs a three-part flight: 1. It accelerates from to over . 2. It cruises at for . 3. It decelerates to a stop over .
Total Distance Calculation: - Phase 1: - Phase 2: - Phase 3: - Total Distance = .
Which of the following describes a change in velocity?
If a drone flies at a constant for , how far does it travel?
In a standard motion profile, the 'Cruise Phase' is characterized by zero acceleration.
Review Tomorrow
In 24 hours, try to explain the difference between speed and velocity to a friend and recall the formula for distance.
Practice Activity
Next time you are in a car or bus, try to identify when you are in the Acceleration, Cruise, and Deceleration phases of the motion profile.