an ant starts at x = 20cm on piece of graph paper and walk alogn the x axis to x = -20cm it then turns around and walks back to x = -10cm determine (a) the ants displacement and (b) the total distance treveled
surely you can trace out the path of the ant on a piece of graph paper ...
(a) -10-20 = -30
(b) |-20-20| + |-10 - (-20)| = 40+10 = 50
it walked 40 left, then 10 right
(a) The ant's displacement is the straight-line distance between its starting point and its final position. In this case, the ant starts at x = 20cm and walks to x = -10cm. The displacement can be calculated by subtracting the initial position from the final position:
Displacement = Final position - Initial position
= (-10cm) - (20cm)
= -10cm - 20cm
= -30cm
Therefore, the ant's displacement is -30cm.
(b) To determine the total distance traveled, we need to consider the entire path the ant took. The ant walked from x = 20cm to x = -20cm and then turned around and walked back to x = -10cm.
The distance traveled is the sum of the distances covered in each leg of the journey, without taking direction into account. The lengths of the legs are:
Leg 1: x = 20cm to x = -20cm (total distance = 20cm + 20cm = 40cm)
Leg 2: x = -20cm to x = -10cm (total distance = 20cm)
Total Distance = Leg 1 + Leg 2
= 40cm + 20cm
= 60cm
Therefore, the total distance traveled by the ant is 60cm.
To determine the ant's displacement and total distance traveled, we can break down the ant's journey into two separate parts: from x = 20cm to x = -20cm, and then from x = -20cm back to x = -10cm.
(a) The ant's displacement:
The displacement is the straight-line distance between the starting point and the ending point. In this case, the ant starts at x = 20cm and ends at x = -10cm. To find the displacement, we calculate the difference between the final position and the initial position:
Displacement = Final Position - Initial Position
Displacement = (-10cm) - (20cm)
Displacement = -10cm - 20cm
Displacement = -30cm
The ant's displacement is -30cm.
(b) The total distance traveled:
To calculate the total distance traveled, we need to sum up the distances covered during each part of the journey.
Part 1: From x = 20cm to x = -20cm.
The distance covered in this part is the absolute value of the displacement, as the ant travels in a straight line:
Distance (Part 1) = |Displacement|
Distance (Part 1) = |-30cm|
Distance (Part 1) = 30cm
Part 2: From x = -20cm back to x = -10cm.
To calculate the distance covered in this part, we subtract the initial position of x = -20cm from the ending position of x = -10cm:
Distance (Part 2) = Final Position - Initial Position
Distance (Part 2) = (-10cm) - (-20cm)
Distance (Part 2) = (-10cm) + (20cm)
Distance (Part 2) = 10cm
Total Distance Traveled = Distance (Part 1) + Distance (Part 2)
Total Distance Traveled = 30cm + 10cm
Total Distance Traveled = 40cm
The ant's total distance traveled is 40cm.
To determine the ant's displacement and total distance traveled, we need to calculate the difference in position between the start and end points and find the total distance covered during the entire journey.
(a) The ant's displacement is the straight-line distance between the start and end points, regardless of the path taken. In this case, the ant starts at x = 20cm and ends at x = -10cm. To find the displacement, we subtract the initial position from the final position:
Displacement = Final position - Initial position
= (-10cm) - (20cm)
= -10cm - 20cm
= -30cm
Therefore, the ant's displacement is -30cm (negative because it moves to the left direction).
(b) To calculate the total distance traveled, we need to consider the entire path the ant covered. The ant moves from x = 20cm to x = -20cm, then turns around and walks back to x = -10cm. We need to find the sum of the distances covered in both legs.
1st leg distance = |Final position - Initial position|
= |-20cm - 20cm|
= |-40cm|
= 40cm
2nd leg distance = |Final position - Initial position|
= |-10cm - (-20cm)|
= |-10cm + 20cm|
= |10cm|
= 10cm
Total distance = 1st leg distance + 2nd leg distance
= 40cm + 10cm
= 50cm
Hence, the ant traveled a total distance of 50cm during its journey.