Vocabulary
This is the distance a car travels during the driver's reaction time.
What is reaction distance?
A car is traveling at 20 m/s and the driver's reaction time is 0.5 seconds. Calculate the reaction distance.
What is 10 meters?
(Solution: 20 m/s × 0.5 s = 10 m)
On a speed versus time graph for a braking car, the line slopes downward from left to right. What does the point where the line reaches zero represent?
What is when the car has come to a complete stop (or stopping time)?
This is why speed limits are lower in school zones compared to highways.
What is children are present and unpredictable, and lower speeds give drivers more time to react and stop safely (shorter reaction and stopping distances)?
In our braking investigation with carts, this was our dependent variable that we measured for each trial.
What is stopping time?
This is the friction force applied to a car when the driver presses the brakes.
What is braking force?
Write the equation we use to calculate stopping time, and identify what each variable represents.
What is Δt = (m × Δv) / F, where Δt is stopping time, m is mass, Δv is change in speed, and F is braking force?
In a force body diagram for a car that is braking, in which direction does the braking force arrow point?
What is backward (or opposite to the direction of motion)?
Explain why distracted driving (like texting) increases the risk of accidents in terms of reaction distance.
What is distraction increases reaction time, which increases reaction distance, meaning the car travels farther before the driver even starts braking?
Name one advantage and one disadvantage of using a computer simulation compared to the physical cart experiment.
What is (advantage) can test many conditions quickly, no measurement errors, can use realistic values, safer OR (disadvantage) not real-world data, computer model limitations, can't observe real physics directly?
In an experiment, this is the variable that changes as a result of changing the independent variable. In our braking investigation, it was the stopping time.
What is the dependent variable?
A car with mass 1,000 kg is traveling at 25 m/s. The driver applies a braking force of 5,000 N. Calculate the stopping time.
What is 5 seconds?
(Solution: Δt = (1,000 kg × 25 m/s) / 5,000 N = 25,000 / 5,000 = 5 seconds)
Two cars are shown on the same speed vs. time graph. Car A's line is steeper than Car B's line. Which car is experiencing more braking force, and how do you know?
What is Car A, because a steeper line means the car is slowing down faster, which indicates more braking force?
A fully loaded delivery truck has much more mass than an empty truck. Using physics concepts, explain why this makes the truck more dangerous when traveling at highway speeds.
What is more mass means longer stopping time with the same braking force, so the truck travels farther before stopping and has less time to avoid collisions?
During the cart investigation, different groups got slightly different results for the same conditions. Name two factors that could explain these differences.
What are (any two of): measurement errors, timing accuracy, friction variations, starting position differences, track imperfections, or human reaction time in measurements?
This type of relationship exists when doubling one variable causes the other variable to be cut in half, like the relationship between braking force and stopping time.
What is an inverse relationship?
A truck has mass 2,400 kg, is traveling at 30 m/s, and needs to stop in 3 seconds. Calculate the minimum braking force needed.
What is 24,000 N?
(Solution: Rearrange to F = (m × Δv) / Δt = (2,400 kg × 30 m/s) / 3 s = 72,000 / 3 = 24,000 N)
You plot mass on the x-axis and stopping time on the y-axis for three trials: (2 kg, 2 s), (4 kg, 4 s), (6 kg, 6 s). Describe what the graph looks like and explain what it tells you about the relationship.
What is a straight line through the origin, showing a linear positive relationship where stopping time increases proportionally with mass?
Name and explain two engineering solutions (besides speed limits) that communities use to improve road safety.
What are (any two of): speed bumps (force drivers to slow down), traffic lights (control traffic flow), better road signage (increase awareness), improved lighting (increase visibility), anti-lock braking systems/ABS (improve braking force), or road widening (more space to maneuver)?
You collect this data: Braking Force of 3,000 N gives 4 seconds stopping time; 6,000 N gives 2 seconds; 12,000 N gives 1 second. What type of relationship does this show, and predict the stopping time for 24,000 N.
What is an inverse relationship, and 0.5 seconds (or half a second)?
Name all three independent variables we investigated that affect a vehicle's stopping time.
What are mass, speed (or initial speed/change in speed), and braking force?
DAILY DOUBLE! A car's stopping time is 6 seconds. Predict the new stopping time if the mass is doubled, the speed is tripled, and the braking force is quadrupled (multiplied by 4).
What is 9 seconds?
(Solution: Original time × 2 × 3 / 4 = 6 × 2 × 3 / 4 = 6 × 6 / 4 = 36 / 4 = 9 seconds)
On a speed vs. time graph, a car starts at 30 m/s and stops in 5 seconds. Draw or describe what happens to the graph if the braking force is doubled but everything else stays the same.
What is the line would still start at 30 m/s but would be steeper and reach zero at 2.5 seconds instead of 5 seconds?
DAILY DOUBLE! A new electric vehicle has 50% more mass than a gas car but also has a braking system that provides 50% more braking force. Using the mathematical model, explain whether the electric vehicle will have a longer, shorter, or equal stopping time compared to the gas car at the same speed.
What is equal stopping time, because the increases in mass and braking force cancel each other out (1.5m × v) / 1.5F = (m × v) / F?
Design a new investigation to test whether wet roads affect stopping time. State your independent variable, dependent variable, and at least two controlled variables.
What is: Independent variable = road condition (wet vs. dry); Dependent variable = stopping time; Controlled variables = mass, initial speed, braking force, type of surface/material, angle of track?