GCSE Mathematics Worksheet - Compound Measures-1-Notes

Distance-time graphs

• In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.
• If an object is accelerating or decelerating, its speed can be calculated at any particular time by:    
• drawing a tangent to the curve at that time
• measuring the gradient of the tangent

Velocity-time graphs

• The gradient of the line is equal to the acceleration of the object.
• The displacement of an object can be calculated from the area under a velocity-time graph.         

       
Acceleration

• Acceleration is the rate of change of velocity. It is the amount that velocity changes per unit time.
• The change in velocity can be calculated using the equation:

• change in velocity = final velocity - initial velocity

     

• The average acceleration of an object can be calculated using the equation:

        
     This is when:

• acceleration (α) is measured in metres per second squared (m/s²)

• change in velocity (∆v) is measured in metres per second (m/s)

• time taken (t) is measured in seconds (s)

• If an object is slowing down, it is decelerating (and its acceleration has a negative value).

Velocity, acceleration and distance

• This equation applies to objects in uniform acceleration:

      (final velocity)2 - (initial velocity) 2  = 2 × acceleration × distance

       

• This is when:

• final velocity (v) is measured in metres per second (m/s)

• initial velocity (u) is measured in metres per second (m/s)

• acceleration (a) is measured in metres per second squared (m/s2)

• displacement (s) is measured in metres (m)          

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