1. During a training session, an athlete runs 140 m West along a straight road (A to B). He then runs 100 m East (B to C) and then finally 60 m East (C to D). The total time taken for this session is 2.5 seconds.
1.1 Draw a vector diagram to represent the three displacements (A to B, B to C, and C to D).
1.2 On the vector diagram, draw and indicate the resultant displacement.
1.3 Calculate the total distance covered by the athlete.
1.4 Determine the change in position at D, relative to A.
1.5 Calculate the average velocity of the athlete.
Answer (2)
1.1 Vector Diagram :
To draw a vector diagram of the athlete's displacements, represent each segment of the run as a vector.
A to B : A vector of 140 m pointing West.
B to C : A vector of 100 m pointing East.
C to D : Another vector of 60 m pointing East.
You can visually align them by starting from point A and ending at point D.
1.2 Resultant Displacement :
Begin at point A (origin) and, by using vector addition, subtract the Eastward run from the Westward run.
Resultant displacement is from the starting point A to the final position at D.
140 m West - (100 m East + 60 m East) = 140 m West - 160 m East = 20 m East.
So, the resultant vector is 20 m East from point A.
1.3 Total Distance Covered :
The total distance covered by the athlete is the sum of all the distances run, regardless of direction.
140 m + 100 m + 60 m = 300 m
1.4 Change in Position at D Relative to A :
The change in position (also known as displacement) is a vector quantity that considers direction.
As calculated, the displacement from A to D is 20 m East.
1.5 Average Velocity :
Average velocity is the total displacement divided by the total time taken.
Average Velocity = Time Displacement
Given that the displacement is 20 m East and the total time is 2.5 seconds:
Average Velocity = 2.5 s 20 m East = 8 m/s East
The average velocity of the athlete is 8 m/s towards the East.
The athlete's total distance covered is 300 m, and their resultant displacement from A to D is 20 m East. The average velocity of the athlete during the workout is 8 m/s East. The vector diagram can visually represent these displacements and resultant.
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