Example of Graphical Representation of Motion

• To determine the speed of an object using a distance-time graph, one can take the following steps:
• Identify Two Points: Let’s consider two points, A and B, on the distance-time graph.
• Draw Parallel Lines: From point A, draw a line parallel to the x-axis, and from point B, draw another line parallel to the y-axis. 
• These lines intersect at a point, C, forming a triangle ABC.
• Determine Time and Distance: On the graph:
  • The horizontal line segment AC represents the time interval (t₂​−t₁)​.
  • The vertical line segment BC indicates the change in distance (s₂​−s₁)​.
• Calculate Speed: As the object moves from point A to point B, the change in its position is (s₂​−s₂) over the time interval (t₂​−t₁)​. 
• Therefore, the object’s average speed v during this interval is given by:

v =  s₂​−s₁/t₂​−t₁

Furthermore, distance-time graphs can also represent accelerated motion. For example, Table 1.1 illustrates distances covered by a car every two seconds, demonstrating an accelerated motion.

Understand the graphical representation of motion Through an Example:

• Above velocity-time graph is for a car moving at a consistent speed of 40 km/h. 
• For objects moving at uniform velocity, the product of their velocity and time yields the displacement. 
• Consequently, the area between the velocity-time graph and the time axis represents the total displacement.
• To ascertain the distance covered by the car between the time intervals t₁​ and t₂​ using the above graph one should:
  • Draw Perpendicular Lines: From the points corresponding to times  t₁​ and t₂​ on the graph, draw perpendicular lines to the opposite axes.
  • Identify Graph Dimensions: The consistent velocity of 40 km/h is depicted by the vertical height (either AC or BD). Meanwhile, the horizontal distance AB represents the time interval t₂​−t₁
  • Calculate Distance: The distance the car traverses in the duration t₂​−t is given by:

s = AC CD 

= [(40 km h-1) (t₂​−t₁)h] 

= 40(t₂​−t₁)km. This distance corresponds to the area of the rectangle ABCD.

• Additionally, to understand uniformly accelerated motion, consider a velocity-time graph. 
• Envision a scenario where a car undergoes an engine test on a straight road. 
• An observer in the car logs the vehicle’s speed every 5 seconds using its speedometer. 
• Above table then showcases the car’s velocity in both km/h and m/s at various time snapshots.