Speed, velocity and acceleration

Speed, velocity and acceleration

1. Average speed

   • Average speed = distance moved/time taken
     • Where:
       • Average speed is measured in metres per second (m/s)
       • Distance moved is measured in metres (m)
       • Time taken is measured in seconds (s)
   • When an object moves in a straight line at a steady speed, it's average speed can be calculated if the distance moved and time taken is known
   • Example:
     • A car travels 300 metres in 20 seconds
       • It's average speed is 300/20 = 15m/s
   • To calculate the motion of everyday objects (eg tennis balls):
     • 1) Measure the distance that the object travels in metres
       • 2) Measure the time it takes for the object to move that distance
         • 3) Use the equation to calculate the average speed

2. Distance-time Graphs

   • It shows how far something travels over a period of time
     • The vertical axis shows the distance traveled from the start
     • The horizontal axis shows the time from the start
     • When an object is stationary , the line on the graph stays horizontal
       • When an object is moving at a steady speed, the line is straight but sloped
         • The steeper the line, the faster an object is travelling

3. Acceleration

   • Acceleration can be calculated from its change in velocity and the time taken
     • Velocity is different to speed
       • It has direction as well as speed
         • Velocities are + (forwards) and - (backwards)
           • Example:
             • -15m/s means moving backwards by 15 metres every second
   • When an object moves in a straight line with a constant acceleration, it's acceleration can be calculated if the change in velocity and how long it takes is known
     • Acceleration (m/s2) = change in velocity (m/s)/ time taken (s)
       • Acceleration units can be written as m/s/s
         • a = (v-u)/t
           • Where:
             • a = acceleration
             • v = final velocity
             • u = initial velocity
             • t = time in seconds
       • Example:
         • A car accelerates in 5 s from 25 m/s to 35 m/s. It's velocity changes 35-25 = 10 m/s. tehrefore it's acceleration is 10/5 = 2m/s/s
   • Deceleration is observed when an object slows down
     • Units are the same but the number has a negative symbol before it
       • Example:
         • The car slowed down at -1m/s

4. Velocity-time Graphs

   • The velocity of an object is its speed in a particular direction
     • Two cars travelling at the same speed but in different directions have different velocities
   • A velocity-time graph shows the speed and direction an object travels over a specific period of time. Velocity-time graphs are also called speed-time graphs
     • The vertical axis of a velocity-time graph is the velocity of the object
     • The horizontal axis is the time from the start
   • When an object is moving with a constant velocity, the line on the graph is horizontal
     • When the horizontal line is at zero velocity, the object is at rest
       • Curved lines on velocity-time graphs also show changes in velocity, but not with a constant acceleration or deceleration
         • The steeper the line, the greater the acceleration of the object
           • A line sloping downwards, with a negative gradient, represents an object with a constant deceleration
             • The acceleration (gradient of the line) can be calculated by change in velocity/time taken
               • E.g. 10/2 = 5m/s/s
     • When an object is undergoing constant acceleration, the line on the graph is straight but sloped
   • The area under the line in velocity-time graph represents the distance traveled
     • To find the distance traveled in the graph, you need to find the area of the light-blue triangle and the dark-blue rectangle
       • Area of light-blue triangle
         • The width of the triangle is 4 seconds and the height is 8 metres per second
           • Area of triangle = 1/2 x base x height
           • So the area of the light-blue triangle is 1/2 x 8 x 4 = 16m
       • Area of the dark-blue rectangle
         • The width of the rectangle is 6 seconds and the height is 8 metres per second
           • The area is 8 x 6 = 48m
       • Area under the whole graph
         • 16 + 48 = 64m
           • This is the total area under the distance-time graph
             • This area is the distance covered

5. Scalar and vector quantities

   • A quantity that has magnitude but no particular direction is described as scalar
     • A quantity that has magnitude and acts in a particular direction is described as vector
       • Vector quantites have both magnitude and direction
         • For example: 11m east and 15 ms-1 at 30 degrees to the horizontal are both vector quantities
           • Vector quantities include:
             • Displacement, velocity, acceleration, force, weight, momentum
               • They change when:
                 • Their magnitude changes, their direction changes and their magnitude and direction both change
                   • Speed is a scalar quantity
                     • It is the rate of change in the distance traveled by an object
                     • Velocity is a vector quantity
                       • It is the speed of an object in a particular direction
     • Scalar quantities only have magnitude (size)
       • For example, 11m and 15ms-1 are both scalar quantities
         • Scalar quantities include:
           • Distance, speed, time, power, energy
             • Scalar quantities change when their magnitude changes

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