Question

A blue line with 5 orange tick marks then one red tick mark then 4 orange tick marks. The number zero is above the red tick mark.
Assume each tick mark represents 1 cm.

Calculate the total displacement from 0 if an object moves 3 cm to the left, then 7 cm to the right, and then 6 cm to the left.

The object moves
cm to the left.

What is the total distance the object travels?
cm

Answer 1

To calculate the total displacement, we can follow the movements of the object step by step:

1. The object moves 3 cm to the left:
- Displacement: -3 cm (since left is negative)

2. Then it moves 7 cm to the right:
- Displacement: +7 cm (since right is positive)

3. Finally, it moves 6 cm to the left:
- Displacement: -6 cm (since left is negative)

Now, we can calculate the total displacement:
\[
\text{Total displacement} = -3\, \text{cm} + 7\, \text{cm} - 6\, \text{cm}
\]
\[
\text{Total displacement} = 7 - 3 - 6 = -2\, \text{cm}
\]

The total displacement from the starting point (0) is **-2 cm**, which means the object ends up 2 cm to the left of the starting position.

Next, we calculate the total distance traveled:

1. The distance for the first move (3 cm to the left) = 3 cm
2. The distance for the second move (7 cm to the right) = 7 cm
3. The distance for the third move (6 cm to the left) = 6 cm

Total distance is the sum of all distances (regardless of direction):
\[
\text{Total distance} = 3\, \text{cm} + 7\, \text{cm} + 6\, \text{cm} = 16\, \text{cm}
\]

Therefore, the answers are:
- The object moves **2 cm** to the left.
- The total distance the object travels is **16 cm**.