Graphical Method Examples

Graphical Method Examples

Example 1.

There is a chair and a boy. The boy can either walk to the left or to the right of the chair. We want to sketch some graphs of the displacement of the boy from the chair. When the boy is at the chair, his displacement is zero.

Take the right side as the positive direction. Sketch a displacement-time graph for each of the following cases:

(a) The boy is 3 m to the right of the chair. He just stands there.
(b) The boy starts at the chair and walks 3 m to the right in 5 s, at uniform velocity.
(c) The boy is at rest at 2 m to the left of the chair.
(d) The boy starts 2 m to the left of the chair and walks to the chair in 3 s, at uniform velocity.

Answer.

Example 2.

There is a girl and a chair. She can either walk to the left or to the right of the chair. Take the right side as the positive direction. Sketch a velocity-time graph for each of the following cases:

(a) She is 3 m to the right of the chair, and just stands there.
(b) She runs to the right at a velocity of 3 m/s.
(c) She walks to the left at a velocity of 1 m/s.
(d) She starts from rest and runs to the right. She increases her velocity uniformly to 4 m/s in 10 s.

Answer.

Example 3.

There is a car. It can move left or right along a road. Take the right side as the positive direction. Sketch an acceleration-time graph for each of the following cases:

(a) The car just rests there.
(b) The car moves at a constant velocity of 10 m/s to the right.
(c) The car moves to the right. Its velocity increases uniformly at 2 m/s².
(d) The car moves to the right. Every second, its velocity decreases by 1 m/s.

Answer.

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