Physics 1 - 1D Kinematics

What is the definition of distance?

The total path length traveled by an object, regardless of direction. Units: meters (m).

What is the definition of displacement?

The net change in position from start to finish, including direction. Units: meters (m).

What is the definition of speed?

The rate at which distance is covered, without direction. Units: meters per second (m/s).

What is the definition of velocity?

The rate at which displacement changes, including direction. Units: meters per second (m/s).

What is the definition of acceleration?

The rate at which velocity changes, including direction. Units: meters per second squared (m/s^2).

What is the difference between distance and displacement?

Distance is the total path length (scalar), while displacement is the straight-line net change in position with direction (vector). E.g., running a 400 m lap gives 400 m distance but 0 m displacement if back at start.

What is the difference between speed and velocity?

Speed is the rate of distance traveled (scalar), while velocity is the rate of displacement with direction (vector). E.g., 10 m/s speed vs. +10 m/s or -10 m/s velocity.

What is the first key equation for 1-D kinematics?

vf = vi + a t (final velocity = initial velocity + acceleration x time).

What is the second key equation for 1-D kinematics?

Delta x = v_i t + 1/2 a t^2 (displacement = initial velocity x time + 1/2 acceleration x time^2).

What is the third key equation for 1-D kinematics?

vf^2 = vi^2 + 2 a Delta x (final velocity^2 = initial velocity^2 + 2 x acceleration x displacement).

What is the fourth key equation for 1-D kinematics?

v_avg = Delta x / t (average velocity = displacement / time).

What makes multi-stage motion problems tricky?

Objects change speed or direction in stages, requiring you to break motion into segments and calculate each separately.

How do you handle missing time or distance in problems?

Use vf^2 = vi^2 + 2aΔx to find acceleration or displacement, then vf = vi + at for time.

Why are negative values and direction tricky?

Forgetting to account for direction can flip answers; acceleration is negative if speed decreases.

How do you interpret graphs in kinematics?

Slope of position vs. time = velocity; slope of velocity vs. time = acceleration; area under velocity vs. time = displacement.

What makes unit conversions tricky?

Mixing units (e.g., km/hr with m/s) requires conversion before solving.

How do you avoid forgetting the square in acceleration?

Check units after solving—velocity/time = m/s^2—and write it out to reinforce.

What is an example of a multi-stage motion problem?

A toy car accelerates for 4 s, coasts for 3 s, then decelerates for 2 s.

What is an example of a missing time problem?

A skateboarder reaches 8 m/s from rest over 16 m; find acceleration and time.

What is an example of a negative acceleration problem?

A car slows from 30 m/s to 10 m/s in 15 s.

What is the acceleration of a helicopter flying at 10 m/s that reaches -32 m/s after 6 seconds?

Acceleration = (final velocity - initial velocity) / time = (-32 m/s - 10 m/s) / 6 s = -42 m/s / 6 s = -7 m/s²

What is the displacement of the helicopter with an initial velocity of 10 m/s, final velocity of -32 m/s, and time of 6 seconds?

Displacement = (initial velocity + final velocity) / 2 * time = (10 m/s + (-32 m/s)) / 2 * 6 s = -11 m/s * 6 s = -66 m

What is the distance the helicopter flies with an initial velocity of 10 m/s, final velocity of -32 m/s, time of 6 seconds, and acceleration of -7 m/s²?

Distance = |displacement| = |-66 m| = 66 m

How long will it take Leo, walking at 1.1 m/s and accelerating at 0.2 m/s², to cover 67 m to physics class?

Use s = ut + (1/2)at², solve quadratic equation 0.1t² + 1.1t - 67 = 0, t ≈ 21.74 s

How long will it take a rock thrown upwards at 1.8 m/s to reach the top of its throw?

Time to top = initial velocity / gravitational acceleration = 1.8 m/s / 9.8 m/s² ≈ 0.1837 s

How long will it take a rock thrown upwards at 1.8 m/s to fall back to its starting point?

Total time = 2 * time to top = 2 * 0.1837 s ≈ 0.3673 s

What was Stephen's speed at the top of a hill if he covers 125 m in 13 s with a final speed of 14 m/s?

Initial velocity = (2 * displacement / time) - final velocity = (2 * 125 m / 13 s) - 14 m/s ≈ 5.23 m/s

What is Stephen's acceleration if he covers 125 m in 13 s with an initial speed of 5.23 m/s and final speed of 14 m/s?

Acceleration = (final velocity - initial velocity) / time = (14 m/s - 5.23 m/s) / 13 s ≈ 0.675 m/s²