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Chapter 2: Q4PE (page 82)

Find the following for path D in Figure 2.59:

(a) The distance travelled.

(b) The magnitude of the displacement from start to finish.

(c) The displacement from start to finish.

Short Answer

Expert verified

a) 8 m

b) 4 m

c) -4 m

Step by step solution

01

Distance and displacement

The distance is the whole length of the body's journey. The meter is the unit of measurement. It's a number that represents a scalar value.

The shortest distance between the beginning and finishing points is defined as displacement. It's a quantity that's been given a vector. The length is given in meters.

The distance and displacement will be the same only if the voyage is in a straight line.

02

For particle D distance and displacement

Figure: Path of particle D

a. The distance travelled by the particle D is :


First, it goes fromx=9鈥�mtox=3鈥�m. The total distance covered is 6m. Then the body comes back till 5m, so it covers more distance. Now the total distance will be 6+2=8鈥尘.

Thus, the distance covered by particle D is 8m.

b. The magnitude of the displacement, in this case, will not be the same as the distance as it is not a straight path.


Displacement of the particle D =Final position 鈥� Initial Position

=5鈥尘鈭�9鈥尘=鈭�4鈥尘


Thus, the magnitude will be 4 m.



c. The direction of the displacement would be -4mas the body is moving in the negative x-direction.

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