Distance, Time, Speed & Acceleration
The Outcomes Being Assessed:
1. Define average speed as total distance travelled divided by total time taken.
2. Solve problems using the equation:
Speed = distance / time
3. Draw and interpret distance time graphs of travelling vehicles.
4. Define acceleration as the change in speed divided by the time taken.
5. Solve problems using the equation:
Acceleration = change in speed / time
6. Draw and interpret speed time graphs of travelling vehicles.
1. Define average speed as total distance travelled divided by total time taken.
2. Solve problems using the equation:
Speed = distance / time
3. Draw and interpret distance time graphs of travelling vehicles.
4. Define acceleration as the change in speed divided by the time taken.
5. Solve problems using the equation:
Acceleration = change in speed / time
6. Draw and interpret speed time graphs of travelling vehicles.
Average Speed
When most people think of speed, they think of average speed. They think, 'It took this long to travel this far, so I am going this fast.'
Average speed is the total distance travelled divided by the total time taken.
Units are often written as km/h or m/s.
m/s is used more commonly in science, as it is a more exact measurement that is easy to relate to.
Average speed is the total distance travelled divided by the total time taken.
Units are often written as km/h or m/s.
m/s is used more commonly in science, as it is a more exact measurement that is easy to relate to.
Calculating Speed
Speed can be calculated by a formula. That is Speed = Distance/Time.
This formula can also be rearranged to find either time or distance. The three forms that can be used are these:
s = d/t
d = st
t = d/s
In some formulas 'v' is used in the place of 's'. This 'v' refers to velocity, which is slightly different from speed, but is often interchangeable.
Velocity refers to the distance travelled away from a starting point divided by the time taken. This means that if an object or person was to go back to the start, the average velocity would be 0 m/s. However the velocity from the starting point to the point where they turned around would still be positive, as would the returning velocity. But the average velocity would be calculated from the idea that the object had not ended up elsewhere.
This formula can also be rearranged to find either time or distance. The three forms that can be used are these:
s = d/t
d = st
t = d/s
In some formulas 'v' is used in the place of 's'. This 'v' refers to velocity, which is slightly different from speed, but is often interchangeable.
Velocity refers to the distance travelled away from a starting point divided by the time taken. This means that if an object or person was to go back to the start, the average velocity would be 0 m/s. However the velocity from the starting point to the point where they turned around would still be positive, as would the returning velocity. But the average velocity would be calculated from the idea that the object had not ended up elsewhere.
Distance Time Graphs
Distance Time Graphs show the movement of an object over time. It only displays 2D movement, or movement of one dimension - to or from the starting point.
Let the object be a vehicle such as a car. A straight line means that the car is moving at a constant speed, this is either stationary (still) or moving. If the line is diagonal, the car is moving. If the line is horizontal then the car is not moving. A vertical line is not possible as it would be as if the car was moving and no time was passing. If a line has a steep gradient, it is moving fast. If the line is not steep, then it is moving slower. You could think like this, if the line is more vertical it is faster, if the line is more horizontal it is slower. A line that has a positive gradient (moving away from the x-axis) means the car is moving away from the starting point. A negative gradient (moving towards the x-axis) shows the car is moving towards the starting point. A line that is curved means a change in speed. This means the car is either accelerating or decelerating. A line becoming more vertical is becoming fast; a line becoming more horizontal is getting slower. |
Acceleration
The formula for acceleration is: Acceleration = (Change in Speed) / (Change in Time or Time Taken)
This is written as ( v2 - v1 )
A = –––––––––
( t2 - t1 )
Acceleration is measured in m/s/s or ms^-2. These units can be changed, however m/s/s is used for scientific purposes, such as consistency and accuracy.
Note that acceleration can only occur when a force is acting upon an object. As soon as the force stops acting on the object, such as when a ball leaves the racket, the object stops accelerating.
Practice using this formula to understand how to measure acceleration. If you measure from beginning to end then you have the average acceleration. If you work with only a segment of the data, then you measuring instantaneous acceleration.
This is written as ( v2 - v1 )
A = –––––––––
( t2 - t1 )
Acceleration is measured in m/s/s or ms^-2. These units can be changed, however m/s/s is used for scientific purposes, such as consistency and accuracy.
Note that acceleration can only occur when a force is acting upon an object. As soon as the force stops acting on the object, such as when a ball leaves the racket, the object stops accelerating.
Practice using this formula to understand how to measure acceleration. If you measure from beginning to end then you have the average acceleration. If you work with only a segment of the data, then you measuring instantaneous acceleration.
Speed Time Graphs