Displacement and Distance:
In order to understand how the concept of motion works, we must first understand the difference between displacement and distance. Distance is determined by how far an object has traveled and is represented by d. While displacement is determined by finding the change in position of an object in a given distance and is represented by s.
Velocity and Speed:
In physics, velocity and speed are different terms. The average speed of an object is determined by dividing the total distance the object has travelled over the time taken.
Average Speed = Total distance travelled
While the velocity of an object at a single point in time is found by dividing the displacement of the object over the time taken.
Instantaneous velocity = displacement
The velocity of an object is represented by v and is given in metres per second (m/s). The average velocity of an object can be found by using the formula:
Average velocity = vav = Δs = change in displacement
Δt change in time
This formula can also be rearranged to give us formulas to find the displacement of the object and the time taken from the average velocity.
Acceleration is when an object 'speeds up', meaning that the velocity of the object is increasing. While deceleration is when an object 'slows down', meaning that the velocity of the object is decreasing. The acceleration of an object can be found by using the formula:
Acceleration = a = Δv = change in velocity = final velocity - initial velocity
Δt time taken time taken
If the acceleration value found using this formula is positive, then it can be said that the object is accelerating. However, if the acceleration value found using this formula is negative, then it can be said that the object is decelerating.
1. A toy train is running around a circular track of diameter 120cm. What is its distance travelled and its displacement after:
(a) one-half of a lap
(b) one full lap
(c) two laps
2. A person rides a bicycle to a shop travelling 300m north along a straight road and then travels west for another 400m. If the trip takes 3 minutes, find;
(a) the average speed
(b) the average velocity
3. The fastest car recorded on land can accelerate from rest to 96.5km/h (26.8m/s) in 3.98 seconds. Calculate the acceleration of the car.
In order to make sure that you fully understand the concept of motion, work through the online interactive activites given in the links below. You can complete these activities individually or in a group. However, make sure that you understand how the physics of motion works and how it relates to a real-life roller coaster. Remember, if you get stuck ask you teacher for help!
Extra Materials and Videos:
Here are some extra links and youtube videos that may help you further understand the concept of motion. You can watch as many or as little as you like! Just make sure you feel comfortable in working with the physics of motion and that you are able to understand how these concepts fit into roller coaster physics.
vav = s/t or s = vavt or t = s/vav