Speed-Time Graphs

 

7.2  Speed-Time Graphs 
 
  In a speed-time graph  
     
   
     
 
  • the vertical axis represents the speed of a motion 
 
     
 
  • the horizontal axis represents the time taken 
 
     
 
  • the gradient of graph represents the rate of change of speed with respect to time, that is acceleration 
 
 
A speed-time graph can be drawn if following information regarding the motion is obtained 
 
  • Speed-time table 
 
  • Equation that represents the relationship between speed and time 
 
  Example  
     
   
     
 

\(P\)

  • The speed of object increases from \(0 \space ms^-1\) to  \(16 \space ms^-1\)
  • The gradient of graph is positive, hence the rate of change of speed is positive 
  • \(\text{Acceleration} = \dfrac{\text{Change of speed}}{\text{Changein time}}\)
  • The area of triangle \(OAP\) that is the area represents the distance travelled in the period of \(10s\)
 
     
 

\(Q\)

  • There is no change of speed (zero gradient)
  • The object moves at a uniform speed
  • The area of square under \(Q\) represents the distance travelled in the period of \((20-10)s\)
 
     
 

\(R\)

  • Speed of the object decreases 
  • The gradient of graph is negative, hence the rate of change of speed is negative 
  • \(\text{Deceleration} = \dfrac{\text{Change of speed}}{\text{Change in time}}\)
  • There is no change in direction in which the motion of the object remains in the same direction 
  •  The area of triangle \(BCR\) that is the area represents the distance travelled in the period of \((25-20)s\)
 
 
 
 

Speed-Time Graphs

 

7.2  Speed-Time Graphs 
 
  In a speed-time graph  
     
   
     
 
  • the vertical axis represents the speed of a motion 
 
     
 
  • the horizontal axis represents the time taken 
 
     
 
  • the gradient of graph represents the rate of change of speed with respect to time, that is acceleration 
 
 
A speed-time graph can be drawn if following information regarding the motion is obtained 
 
  • Speed-time table 
 
  • Equation that represents the relationship between speed and time 
 
  Example  
     
   
     
 

\(P\)

  • The speed of object increases from \(0 \space ms^-1\) to  \(16 \space ms^-1\)
  • The gradient of graph is positive, hence the rate of change of speed is positive 
  • \(\text{Acceleration} = \dfrac{\text{Change of speed}}{\text{Changein time}}\)
  • The area of triangle \(OAP\) that is the area represents the distance travelled in the period of \(10s\)
 
     
 

\(Q\)

  • There is no change of speed (zero gradient)
  • The object moves at a uniform speed
  • The area of square under \(Q\) represents the distance travelled in the period of \((20-10)s\)
 
     
 

\(R\)

  • Speed of the object decreases 
  • The gradient of graph is negative, hence the rate of change of speed is negative 
  • \(\text{Deceleration} = \dfrac{\text{Change of speed}}{\text{Change in time}}\)
  • There is no change in direction in which the motion of the object remains in the same direction 
  •  The area of triangle \(BCR\) that is the area represents the distance travelled in the period of \((25-20)s\)