Vectors & Scalars
The two quantities that vectors have:
Direction and magnitude
A train covers 300 m in 20 s. Calculate the average speed.
What is 15 m/s?
A horizontal line on a distance-time graph shows this.
Answer: What is stationary or not moving?
A car increases its speed from 0 m/s to 10 m/s in 5 s. What is its acceleration?
Answer: What is 2 m/s²?
Force is calculated using this formula:
Force = mass × acceleration
F = m a
Speed is an example of a _____ quantity, while displacement is an example of a _____ quantity.
scalar and vector
A car drives 120 km north in 2 hours, then 90 km south in 1 hour. What is the magnitude of its average velocity?
What is approximately 10 km/h north?
The slope of a distance-time graph shows this.
Answer: What is speed?
A train slows down from 20 m/s to 10 m/s in 5 s. What is the acceleration?
Answer: What is −2 m/s²?
Newton's first law can be described with just one word:
Inertia
A car travels 50 km north and then 30 km south. What are the distance and displacement?
80 km and 20 km north
A runner completes a 400 m circular track in 50 s. Calculate the average speed and average velocity.
What is 8 m/s (speed) and 0 m/s (velocity)?
A horizontal line on a speed-time graph shows this
Constant speed
A bike accelerates uniformly from 3 m/s to 15 m/s in 4 s. Calculate the acceleration.
Answer: What is 3 m/s²?
A football player kicks a ball upwards with 20 N of force. What is the force of the ball on the foot?
20 N downwards
An object moves in a circle at constant speed. Explain why its velocity is changing.
The direction of motion changes, so the velocity vector changes
Why can average speed be higher than average velocity, but not the other way around?
Speed is reliant on distance, whereas velocity is reliant on displacement. If you do not take a direct path, distance will be greater than displacement, meaning speed will be higher than velocity.
A distance–time graph curve that gets steeper over time indicates this.
Answer: What is acceleration?
A car accelerates uniformly from 10 m/s to 30 m/s at 4 m/s². How long does it take to reach 30 m/s?
Answer: What is 5 s?
A 50 kg astronaut is on the Moon (g = 1.6 N/kg). How much gravitation force does she experience?
80 N
A plane flies 300 km east and then 400 km north. What is the magnitude of its displacement?
500 km
A bird flies north for 1 hour at 50 km/h, then south for 4 hours at 10 km/h.
What is its average speed & its average velocity?
Speed: 18 km/h
Velocity: 2 km/h north
Why can't the slope of a distance-time graph ever go downwards?
Distance is a scalar quantity - you cannot travel a negative distance.
A car accelerates at 3 m/s² for 6 seconds and reaches a speed of 21 m/s. What was its speed at the start?
Answer: What is 3 m/s?
A car weighing 1000 kg hits a wall, causing its velocity to go from 72 km/h to 0 km/h in one second. What force did the car experience?
F = m a = 1000 x -20 m/s/s
F = -2000 N