Question

1. Jasmine walks from the back of room 822 to the front. The room has a length of
20 metres
a. What is the distance Jasmine walked?
b. What is the displacement of Jasmine from start to finish?
c. Now Jasmine walks half way back. What is her new total distance walked?
d. What is her new total displacement?

Answer 1

a) 20 metres

b) +20 metres

c) 30 metres

d) +10 metres

Explanation:

a)

Distance is a scalar quantity which represents the total length of the path covered by an object in motion.

Displacement, instead, is a vector quantity connecting the initial position to the final position of motion of the object.

In this problem:

- The length of the room is 20 metres

- Jasmin walked from the back of the room to the front of the room

Therefore, the total length of the path covered by Jasmine is equal to the length of the room, therefore it is:

d = L = 20 metres

b)

As we said before, displacement is a vector connecting the initial position of motion to the final position of motion.

Here we can choose the origin (position zero) as the back of the room, so that

$x_i = 0 m$

is the initial position.

Then, Jasmine walked 20 metres towards the  front; so her final position is

$x_f=+20 m$

Therefore, the displacement is the difference between the initial and final position; it is:

$d=x_f - x_i = +20 -(0)=+20 m$

c)

Here Jasmine walks half way back.

This means that the total distance covered by Jasmine is:

- The full length of the room (to reach the front)

+

- Half length of the room (to come back half way)

So the total distance covered is:

$d=L+\frac{L}{2}$

where

L = 20 m is the length of the room

Substituting, we find the total distance:

$d=20+\frac{20}{2}=30 m$

d)

Here Jasmine walks half way back.

So we have to compute her new displacement.

In this situation, we have:

$x_i = 0 m$

is the initial position, since she started from the back of the room

$x_f=+10 m$

is her final position, since she walked halfway back, so the reaches half of the room as her final position

Therefore, the displacement of Jasmine in this case is:

$d=x_f-x_i = +10 -0 = +10 m$