Explanation: Constant speed means the object covers the same distance in equal time intervals. At 15 m/s, the object moves exactly 15 meters every second. This is the definition of constant speed.

Explanation: Displacement is the change in position from start to finish, measured in a straight line with direction. The runner goes 50 m north, then returns 30 m south. The net displacement is 50 m - 30 m = 20 m north (the starting point was not returned to).

Explanation: Distance is the total length of the path traveled, regardless of direction. The student walks 12 km + 8 km = 20 km total distance. Distance is always positive and doesn't care about direction changes.

Explanation: A vector quantity has both magnitude (size) and direction. Displacement is a vector because it tells us how far AND in what direction. Distance, speed, and average speed are scalar quantities (magnitude only, no direction).

Solution:
What is distance? Distance is the total length of the path traveled, regardless of direction.

Given: Ball rolls 18 m right + 12 m left
Formula: Total Distance = Sum of all path lengths

Calculation:
Distance = 18 m + 12 m = 30 m

Answer: 30 meters (we don't subtract because distance counts ALL motion)

Solution:
What is displacement? Displacement is the straight-line change in position from start to finish, WITH direction.

Given: Ball rolls 18 m right, then 12 m left
Formula: Displacement = Final Position - Initial Position (with direction)

Set up: Let right = positive, left = negative
First motion: +18 m (right)
Second motion: -12 m (left)

Calculation:
Displacement = 18 m + (-12 m) = 18 m - 12 m = 6 m right

Answer: 6 meters to the right

Solution:
Formula: Average Speed = Total Distance ÷ Total Time

Given:
Distance = 240 meters
Time = 16 seconds

Calculation:
Average Speed = 240 m ÷ 16 s
Average Speed = 15 m/s

Answer: 15 m/s means the cyclist travels an average of 15 meters every second.

Solution:
Formula: Distance = Speed × Time

Given:
Speed = 8 m/s
Time = 25 seconds

Calculation:
Distance = 8 m/s × 25 s
Distance = 200 meters

Answer: 200 meters - the penguin travels a total of 200 m in 25 seconds.

Solution:
Formula: Average Speed = Total Distance ÷ Total Time

Given: 5 segments of 1000 m each, with different times for each

Step 1: Find Total Distance
Total Distance = 1000 + 1000 + 1000 + 1000 + 1000 = 5000 m

Step 2: Find Total Time
Total Time = 250 + 260 + 240 + 270 + 280 = 1300 seconds

Step 3: Calculate Average Speed
Average Speed = 5000 m ÷ 1300 s = 3.846... m/s ≈ 3.85 m/s

Answer: 3.85 m/s (rounded to 2 decimal places)

Solution:
Given:
Segment 1: 2000 m at 10 m/s
Segment 2: 1500 m in 75 seconds

Step 1: Find Time for First Segment
Formula: Time = Distance ÷ Speed
Time = 2000 m ÷ 10 m/s = 200 seconds

Step 2: Find Total Distance
Total Distance = 2000 m + 1500 m = 3500 m

Step 3: Find Total Time
Total Time = 200 s + 75 s = 275 seconds

Step 4: Calculate Average Speed
Average Speed = 3500 m ÷ 275 s = 12.727... m/s ≈ 12.73 m/s

Answers: Time = 200 s, Average Speed = 12.73 m/s

Explanation: A person walks 40 m north, then 40 m south. They end up at their starting point. Since displacement measures the straight-line change in position from start to finish, the displacement is 0 meters.

Explanation: Speed is a scalar quantity - it only tells us how fast something is moving. Velocity is a vector quantity - it tells us how fast AND in what direction something is moving. This is the main difference between them.

Explanation: Displacement is the net change in position. Taking east as positive: the plane flies 500 km east, then 300 km west. Net displacement = 500 km - 300 km = 200 km east (final position is 200 km east of the starting point).

Solution:
Formula: Distance = Speed × Time

Given:
Speed = 60 km/h
Time = 3 hours

Calculation:
Distance = 60 km/h × 3 h = 180 kilometers

Answer: 180 km - the car travels 180 km in 3 hours.

Solution:
Formula: Average Speed = Total Distance ÷ Total Time

Given:
Distance = 800 meters
Time = 400 seconds

Calculation:
Average Speed = 800 m ÷ 400 s = 2 m/s

Answer: 2 m/s - the swimmer swims an average of 2 meters per second.

Solution:
Formula: Time = Distance ÷ Speed (rearranged from Distance = Speed × Time)

Given:
Distance = 1500 meters
Speed = 30 m/s

Calculation:
Time = 1500 m ÷ 30 m/s = 50 seconds

Answer: 50 seconds - it takes 50 seconds for the train to travel 1500 meters.

Solution:
Formula: Average Speed = Total Distance ÷ Total Time

Given:
Segment 1: 5 km east in 30 minutes
Segment 2: 3 km west in 20 minutes

Step 1: Find Total Distance
Total Distance = 5 km + 3 km = 8 km (we add because distance counts all motion)

Step 2: Find Total Time (convert to hours)
Total Time = 30 min + 20 min = 50 minutes
Convert to hours: 50 min ÷ 60 min/h = 0.833 hours

Step 3: Calculate Average Speed
Average Speed = 8 km ÷ 0.833 h = 9.6 km/h

Answer: 9.6 km/h (or 9.60 km/h)

Solution:
Formula: Average Velocity = Displacement ÷ Time (with direction!)

Given:
Displacement = 50 meters east
Time = 20 seconds

Calculation:
Average Velocity = 50 m ÷ 20 s = 2.5 m/s

Important: Since displacement includes direction (east), velocity must also include direction.

Answer: 2.5 m/s east

Solution:
Given:
Segment 1: 15 km south at 50 km/h
Segment 2: 25 km north at 75 km/h

Step 1: Find Time for First Segment
Formula: Time = Distance ÷ Speed
Time = 15 km ÷ 50 km/h = 0.3 hours

Step 2: Find Time for Second Segment
Time = 25 km ÷ 75 km/h = 0.333... hours ≈ 0.333 hours

Step 3: Find Total Distance
Total Distance = 15 km + 25 km = 40 km

Step 4: Find Total Time
Total Time = 0.3 h + 0.333 h = 0.633 hours

Step 5: Calculate Average Speed
Average Speed = 40 km ÷ 0.633 h = 63.19... km/h ≈ 63.2 km/h

Answers: Time for first segment = 0.3 h, Average Speed = 63.2 km/h

Solution:
Given:
Segment 1: 600 m at 12 m/s
Segment 2: 400 m in 25 seconds

Step 1: Find Time for First Segment
Formula: Time = Distance ÷ Speed
Time = 600 m ÷ 12 m/s = 50 seconds

Step 2: Find Total Distance
Total Distance = 600 m + 400 m = 1000 meters

Step 3: Find Total Time
Total Time = 50 s + 25 s = 75 seconds

Step 4: Calculate Average Speed
Formula: Average Speed = Total Distance ÷ Total Time
Average Speed = 1000 m ÷ 75 s = 13.333... m/s ≈ 13.33 m/s

Answer: 13.33 m/s