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Let’s calculate displacement using some real-world examples.
Example 1: Constant Velocity
If an object has constant velocity, you can use the velocity formula to calculate displacement. For example, f a car has an average velocity of 25 miles per hour (40 kilometers per hour) and travels for 15 minutes, what is its displacement?
To solve this, we can use the formula:
Where v is 25 miles per hour (40 kilometers per hour) and t is 15 minutes, or 0.25 hours.
d = (25)(0.25) or d = (40)(0.25)
d = 6.25 miles (10 kilometers)
So, after traveling 25 minutes at a constant velocity of 25 miles per hour (40 kilometers per hour), this car has a displacement of 6.25 miles (10 kilometers).
Example 2: Constant Acceleration
If a car traveling at 22.4 miles per hour (36 kilometers per hour) needs to come to a stop within 30 seconds, what would the vehicle’s displacement be?
First, we can calculate the acceleration.
Where v1 is the car’s initial velocity (22.4 miles per hour or 36 kilometers per hour), v is the car’s final velocity (0 miles per hour), and t is the time (30 seconds).
First, let’s do some unit conversion to calculate the acceleration in SI units — meters per seconds squared.
v1 = 36 kilometers per hour
v1 = 36,000 meters per hour
v1 = 10 meters per second
Then we can plug that into our formula:
a = 0.33 meters per second squared
Now that we know the acceleration, we can calculate the displacement.
Where a is acceleration (0.33 meters per second squared), t is time (30 seconds), and v is final velocity (0 meters per second).
d = 1/2(0.33 x 30)2 + (10 x 30)
The car had a displacement of 349.005 meters (1,145 feet) as it came to a stop.
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