1. A farmer moves along the boundary of his rectangular field with sides of 10 m x 20 m. The farmer covers 1 m in 1 second. What will be the magnitude of the displacement after completing the total distance traveled?

2. Rahul pedals his cycle from rest to reach a velocity of 10 m/s in 30 seconds. Then, he applies the brakes such that the velocity of the cycle decreases to 6 m/s in the next 5 seconds. Calculate the acceleration and deceleration.

1). He's walking the 'perimeter' of his field, meaning 'the distance all the way around'. If he stays right along the fence all the way, then the total distance he walks is (10 + 20 + 10 + 20) = 60 meters. (It's a small field ... about 5% of an acre.) The magnitude of displacement is the distance between the start point and end point, regardless of the route. After he finishes one whole trip around, his displacement is zero, because he ends up at the same place where he started. Notice the big fat red herring in the question: None of this depends on the speed at which he walks.
2). Acceleration = (change in speed) / (time for the change)
While speeding up, acceleration = (10 - 0) / 30 = 1/3 meter per second².
While slowing down, deceleration = (6 - 10) / 5 = -4/5 = -0.8 meter per second²

Answered by AL2006 | 2024-06-10

The farmer's displacement after completing a lap around his rectangular field is 0 meters since he returns to the starting point. Rahul's acceleration while reaching 10 m/s is 3 1 ​ m/s 2 , and his deceleration while slowing to 6 m/s is − 0.8 m/s 2 .
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Answered by AL2006 | 2024-12-24