Unit 3: Motion Along a Straight Line
Position, velocity, and acceleration built from calculus and from constant-acceleration shortcuts, ending in free fall.
6 topics · 23 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Position, Displacement, and Distance
- How it worksHow do you read an object's displacement directly off a position-versus-time graph?
- Common mistakeWhy isn't distance traveled the same number as displacement whenever a path doubles back on itself?
- Going furtherWhat happens to displacement, but not distance, when a trip ends exactly where it started?
Your turn1 of 2
A particle starts at x = 0, walks to x = 17 m, then walks back to x = 5 m. What is the total distance traveled, in meters?Average and Instantaneous Velocity
- How it worksHow does shrinking the time interval on a position graph turn an average velocity into an instantaneous one?
- Worked exampleFind the average velocity of a car that goes from x = 2 m to x = 32 m in 5 seconds.
- Common mistakeWhy can an object have a positive velocity and a negative acceleration at the very same instant?
Your turn1 of 2
A car moves from x = 7 m to x = 38 m in 9 s. What is its average velocity, in meters per second?Acceleration in One Dimension
- How it worksHow do you read acceleration off the slope of a velocity-versus-time graph?
- Worked exampleFind the acceleration of a car that speeds up from 10 m/s to 26 m/s in 4 seconds.
- Common mistakeWhy doesn't zero velocity mean an object has zero acceleration at that same instant?
- Going furtherWhat does it mean physically when an object's velocity and acceleration point in opposite directions?
Your turn1 of 2
A car speeds up from 11 m/s to 30 m/s in 8 s. What is its acceleration, in meters per second squared?Kinematics With Constant Acceleration
- How it worksHow do the constant-acceleration equations let you solve for position and velocity without touching calculus?
- Worked exampleFind how far a car travels while accelerating from rest at 3 m/s2 for 6 seconds.
- Worked exampleFind the time it takes a ball thrown downward at 5 m/s to fall 20 m, ignoring air resistance.
- Common mistakeWhy doesn't doubling an object's acceleration time just double the distance it ends up covering?
- Going furtherWhat happens to a car's stopping distance if its initial speed doubles but its braking deceleration stays fixed?
Your turn1 of 2
A car starts from rest and accelerates at 4.63 m/s2 for 8 s. How far does it travel, in meters?Free Fall
- How it worksHow does gravity give every object near Earth's surface the same downward acceleration regardless of its mass?
- Worked exampleFind the speed of a ball 2 seconds after being dropped from rest, taking g = 9.8 m/s2.
- Common mistakeWhy doesn't a heavier ball fall faster than a lighter one dropped from the same height?
- Going furtherWhat changes about free fall on a planet where g is three times Earth's value?
Your turn1 of 2
A ball is dropped from rest and falls for 2.94 s. Taking g = 9.8 m/s2, what is its speed, in meters per second?Motion From Calculus: Derivatives and Integrals
- How it worksHow does taking the derivative of position twice hand you velocity and then acceleration?
- How it worksHow does integrating acceleration over time build up velocity, and integrating velocity build up position?
- Worked exampleFind the velocity and acceleration at t = 2 s for x(t) = 3t3 - 2t2 + 5.
- Ties togetherHow does the area under a velocity-time graph give the same displacement that integrating v(t) gives?
Your turn1 of 2
A particle's position is given by x(t) = 3 t3 - 4 t2 + 5, with x in meters and t in seconds. What is its velocity at t = 3 s?