Speed is a scalar quantity that refers to how fast an object moves. It is the rate at which the object covers distance, and it is always positive or zero. Speed cannot be negative.
For example, if a car travels 2000 m in 250 s, its average speed is 8 m/s. The car’s speed does not consider the direction of its motion, only the magnitude of its displacement over time.
Velocity is a vector quantity that refers to the rate at which an object changes its position. It has both magnitude and direction. Velocity can be positive, negative, or zero, depending on the direction of motion and the starting and ending points.
For example, if a car travels striaght 2000 metres to the north in 250 seconds, its average velocity is 8 m/s to the north. The car’s velocity takes into account both the magnitude of its displacement and the direction in which it is moving.
.Example:
- A car travels 3000 meters in 150 seconds . What is the average speed of the car?
Answer:
The average speed of the car is distance traveled divided by time taken.
Average speed = 3000 meters / 150 seconds = 20 m/s.
- A cyclist travels 15 000 meters to the east in 1800 seconds, and then turns around and travels back 15 000 meters to the west in 2700 seconds. What is the average speed of the cyclist?
Answer:
The total distance traveled by the cyclist is 15 000 meters + 15 000 meters = 30 000 meters
The total time taken by the cyclist is:
1800 seconds + 2700 seconds = 4500 seconds = 75 minutes = 1.25 hours.
Therefore, the average speed of the cyclist is distance travelled divided by time taken.
Average speed = 30 000 meters / 4500 seconds = 6.67 m/s = 24 km/h.
- A train travels 20 kilometers north in 2 hours and then 150 kilometers south in 1.5 hours. What is the average velocity of the train?
Answer:
The total displacement of the train is 200 km north – 150 km south = 50 km north.
The total time taken by the train is 2 hours + 1.5 hours = 3.5 hours.
Therefore, the average velocity of the train is displacement divided by time taken.
Average velocity = 50 km / 3.5 hours = 14.3 km/hour north.
- A boat travels 40 kilometers upstream in 4 hours and then returns downstream in 2.5 hours. If the speed of the current is 5 kilometers per hour, what is the speed of the boat in still water?
Answer:
Let’s call the speed of the boat in still water “v” and the speed of the current “c”.
Upstream speed = v – c
Downstream speed = v + c
Distance upstream = 40 km
Distance downstream = 40 km
Time upstream = 4 hours
Time downstream = 2.5 hours
Using the distance formula: distance = speed x time
40 = (v – 5) x 4 (upstream)
40 = (v + 5) x 2.5 (downstream)
Simplifying the equations, we get:
4v – 20 = 40
2.5v + 12.5 = 40
Solving for v, we get:
v = 15 km/hour
Therefore, the speed of the boat in still water is 15 km/hour.
- A runner sprints 100 meters north in 10 seconds, and then sprints 50 meters south in 5 seconds. What is the average velocity of the runner?
Answer:
The total displacement of the runner is 100 m north – 50 m south = 50 meters north.
The total time taken by the runner is 10 seconds + 5 seconds = 15 seconds.
Therefore, the average velocity of the runner is displacement divided by time taken.
Average velocity = 50 m / 15 seconds = 3.33 m/s north.