Motion Math
Calculate the average speed of an object that travels 60 m in 12 s. Show your calculation.
Average speed = total distance / time = 60 m / 12 s = 5 m/s.
Write a short definition for speed and a short definition for velocity.
Speed: how fast an object moves. Velocity: speed with direction.
On a distance vs.time graph, what does a horizontal (flat) section mean?
Horizontal means the object is at rest (not changing distance).
State Newton’s First Law in one sentence that includes the term inertia.
Newton’s First Law: An object at rest stays at rest and an object in motion stays in motion with the same velocity unless acted on by an unbalanced force (inertia is the tendency to resist changes in motion).
A walker goes 3.5 km in 0.5 hour. What is the average speed in km/h? Show work.
Average speed = 3.5 km / 0.5 h = 7 km/h.
Which of these is a velocity:
a.5 m/s
b.North 5 m/s
c.very fast
d.20 km
Circle the correct choice and explain why.
b. North 5 m/s only — it includes direction, so it is velocity. 5 m/s is speed only.
Sketch (describe) the distance vs. time graph shape for an object that starts at rest, speeds up steadily for 4 seconds, then moves at a constant speed for 6 seconds.
Slope starts at zero then becomes an upward-curving line (increasing slope) for 4 s (acceleration), then a straight line with constant slope for next 6 s (constant speed).
Give an example of balanced forces (real-world) and explain why the object’s motion does not change.
Example: A book lying on a desk remains at rest because the upward normal force balances the downward gravitational force — net force = 0, so motion stays unchanged.
An athlete runs 400 m around a track in 50 s, then stops for 10 s, then runs another 200 m in 25 s. What is the athlete’s average speed for the entire activity? Show calculations.
Total distance = 400 + 200 = 600 m. Total time = 50 + 10 + 25 = 85 s. Average speed = 600 / 85 ≈ 7.06 m/s.
Two cars each travel 100m in 10s along the same straight road. Car A goes east the whole time. Car B goes 50 m east, then turns around and returns 50 m west to its starting point. Compare their speeds and their velocities (displacement and direction)
Both travel same distance/time so speeds = 100 m / 10 s = 10 m/s each. Displacement: Car A: 100 m east → velocity = 10 m/s east. Car B: ends at starting point → displacement = 0 → velocity = 0 m/s. So speeds equal; velocities different.
Complete the sentence: "The more steep a slope on a distance–time graph is, the _____ the object is moving." Then explain in one sentence why slope relates to speed.
The more steep a slope on a distance–time graph is, the faster the object is moving.
Explanation: Slope = rise/run = change in distance divided by change in time, which is the object's speed.
A hockey puck slides on frictionless ice at constant speed. According to Newton’s First Law, what must be true about the net force on the puck? Explain.
Net force must be zero (no unbalanced force); thus the puck maintains constant velocity.
A car travels 90 km at a constant speed in 1.5 hours, then 60 km in 0.75 hours. Find the average speed for the whole trip.
Total distance = 90 + 60 = 150 km. Total time = 1.5 + 0.75 = 2.25 h. Average speed = 150 / 2.25 = 66.67 km/h.
A runner completes one full lap around a circular track (400 m) in 80 s and ends at the starting point. (a) What is the runner’s average speed? (b) What is the runner’s average velocity? Explain why the two answers differ.
(a) Average speed = total distance / time = 400 m / 80 s = 5 m/s. (b) Average velocity = displacement / time. Displacement = 0 m (ended at start), so average velocity = 0 m/s. Explanation: Average speed is based on total distance traveled; average velocity depends on displacement which is zero when returning to the start, so velocity is zero even though speed is positive.
Use the graph on the diagram page. What do you know about the motion of the bicyclist from the graph? List at least three facts supported by the graph (include speed calculation).
Any answers similar will be okay as well.
Describe how unbalanced forces change the state of motion of an object, and give a classroom demonstration idea that shows this effect.
Unbalanced forces produce acceleration (change speed or direction). Demonstration: tug-of-war where one side suddenly pulls harder (unbalanced) and a toy car on a track accelerates when a push (unbalanced force) is applied.
A particle moves along a straight line: 30 m east in 5 s, then 10 m west in 2 s, then 20 m east in 3 s.
Compute (a) total distance, (b) total elapsed time, and (c) average speed.
(a) Total distance = 30 + 10 + 20 = 60 m. (b) Total time = 5 + 2 + 3 = 10 s. (c) Average speed = 60 / 10 = 6 m/s.
A bicyclist travels around a rectangular block 200m east, then 100m north, then 200m west, then 100m south, taking a total of 400s. Calculate the bicyclist’s average speed
Total distance = 200+100+200+100 = 600m. Total time = 400s. Average speed = 600/400 = 1.5m/s. Displacement = 0 (returned to start), so average velocity = 0m/s
On graph paper (or the space provided on your worksheet), draw a distance–time graph that matches this motion description:
Check the white board for the correct answer.
For each scenario below, decide whether it shows balanced forces or unbalanced forces. Mark "Balanced force" or "Unbalanced force"