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Flashcards · AP® Physics 1: Algebra-Based · Unit 1

Unit 1: Kinematics flashcards

34 cards on topics 1.1 to 1.5. Pick a topic or study the whole unit.

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1.1 Scalars and Vectors in One Dimension

What is the difference between a scalar and a vector?
A scalar has magnitude only (distance, speed, time, mass). A vector has magnitude and direction (position, displacement, velocity, acceleration).
How do you write a vector along one axis?
Use its component, such as v_x: a signed number with no arrow. The sign gives the direction relative to the stated axis; the absolute value gives the magnitude, so speed = |v_x|.
How do you add one-dimensional vectors such as displacements?
Give each one its sign from the chosen axis, then add the signed values: sum = d₁ + d₂ + d₃ + … Total distance is different: it adds the sizes, |d₁| + |d₂| + …
With +x east, a cart moves 7.0 m east, 3.0 m west, then 6.0 m west. What are its displacement and distance?
Displacement = +7.0 − 3.0 − 6.0 = −2.0 m, so 2.0 m west. Distance = 7.0 + 3.0 + 6.0 = 16 m.
Which is faster: −8.0 m/s or +5.0 m/s?
−8.0 m/s. The sign only gives direction; its speed is 8.0 m/s. "Negative means small" is a common mistake.
What happens to a vector answer if you reverse the chosen axis?
Every sign flips, but the physical answer (size and real-world direction) does not change. A sign means nothing unless the axis is stated.
What must a vector arrow on a diagram show?
It points in the vector's direction and its length is in proportion to the magnitude, with the scale written on the diagram. A longer arrow must mean a bigger magnitude.

1.2 Displacement, Velocity, and Acceleration

What is the difference between displacement and distance travelled?
Displacement Δx = x − x₀ is the signed change in position. Distance travelled is the total path length and is never negative. They differ whenever the object turns around.
How are average velocity and average speed defined?
Average velocity v_avg = Δx / Δt uses only the start and end positions. Average speed = distance / Δt uses the whole path and is never negative. Both in m/s.
How is average acceleration defined?
a_avg = Δv_x / Δt = (v_x − v_x0) / Δt, in m/s². An object accelerates whenever its velocity changes: speeding up, slowing down or reversing direction.
How do you tell whether an object is speeding up or slowing down?
Compare the signs of v_x and a_x. Same signs: speeding up. Opposite signs: slowing down. Negative acceleration alone does not mean slowing down.
A ball hits a wall at +3.0 m/s and rebounds at −2.0 m/s after 0.10 s of contact. What is its average acceleration?
a_avg = (−2.0 − 3.0) / 0.10 = −50 m/s². Keep the signs: the change in velocity (−5.0 m/s) is bigger than the change in speed.
How do you find instantaneous velocity from a position–time graph?
Take the slope of the tangent line at that instant. A secant slope between two points gives only the average velocity over that interval.
Is acceleration zero when velocity is momentarily zero?
No. At the top of a vertical throw v = 0 but the acceleration is still g downward, because the velocity is still changing.

1.3 Representing Motion

How do you read a motion diagram?
Dots are at equal time intervals. Growing gaps mean speeding up; shrinking gaps mean slowing down. The acceleration arrow shows which way the velocity is changing.
What do the slopes and areas of motion graphs give?
Slope of x–t = v_x. Slope of v_x–t = a_x. Area under v_x–t = Δx (negative below the axis). Area under a_x–t = Δv_x, so add v_x0 for the final velocity.
What are the three constant-acceleration equations, and what does each leave out?
v_x = v_x0 + a_x t (no x). x = x₀ + v_x0 t + ½a_x t² (no v_x). v_x² = v_x0² + 2a_x(x − x₀) (no t). Use them only when a_x is constant.
What is the acceleration of an object in free fall, with +y up?
a_y = −g, with g ≈ 9.8 m/s², on the way up, at the top and on the way down (air resistance ignored, near Earth's surface). Writing a_y = 0 at the top is a common error.
A stone is dropped from rest. How far does it fall in 1.5 s?
Δy = ½gt² = ½ × 9.8 × 1.5² ≈ 11 m.
What does a falling straight line on a v_x–t graph mean?
Constant negative a_x. It does not mean the object is moving backwards; it moves in the −x direction only where the line is below the time axis.
What should you do when acceleration is not constant?
Describe it and sketch it, using slopes and areas of graphs, but do not calculate with the constant-acceleration equations.

1.4 Reference Frames and Relative Motion

What is a reference frame, and what is an inertial frame?
A reference frame is an origin, an axis and a clock belonging to one observer. An inertial frame is not accelerating; treat frames as inertial unless told otherwise.
How do you combine relative velocities along one line?
v_AC = v_AB + v_BC (inner letters match). Swapping subscripts flips the sign: v_BA = −v_AB. From ground values: v_AB = v_AG − v_BG (object first, observer second).
A river flows at +1.0 m/s and a boat moves at 3.0 m/s relative to the water. What is its velocity relative to the bank going downstream and upstream?
Downstream: +3.0 + 1.0 = +4.0 m/s. Upstream: −3.0 + 1.0 = −2.0 m/s (taking +x downstream).
Do different inertial observers measure different accelerations?
No. All inertial observers measure the same acceleration and the same time interval Δt. Only positions, displacements and velocities depend on the frame.
Two objects move towards each other. How fast do they close in on each other?
At the sum of their speeds. Subtract signed velocities (v_AB = v_AG − v_BG), not speeds, so opposite directions add.
Is one observer "wrong" when two observers measure different velocities?
No. Both are right in their own frames. Always name the observer: a velocity has meaning only relative to something.

1.5 Vectors and Motion in Two Dimensions

How do you resolve a vector into components?
With θ measured from the +x axis: A_x = A cos θ, A_y = A sin θ. Use cos for x only when θ is measured from the x-axis.
How do you find the magnitude and direction of a vector from its components?
A = √(A_x² + A_y²) and tan θ = A_y / A_x. Sketch to choose the quadrant, because tan⁻¹ only returns angles between −90° and +90°.
How do you add two vectors in two dimensions?
Add the x-components (R_x = A_x + B_x), add the y-components (R_y = A_y + B_y), then rebuild the resultant with Pythagoras and tan θ. Never add magnitudes directly.
What are the accelerations of a projectile?
a_x = 0 and a_y = −g (with +y up), with air resistance negligible. Treat x and y as two separate one-dimensional motions; only the time t is shared.
What are the velocity and acceleration at the top of a projectile's path?
Only v_y is zero; the speed there is v_x0. The acceleration is still g downward throughout the flight.
A ball rolls off a 0.80 m high table at 2.0 m/s. How long is it in the air and how far away does it land?
t = √(2h/g) = √(2 × 0.80 / 9.8) ≈ 0.40 s. Horizontal distance = v_x0 t = 2.0 × 0.404 ≈ 0.81 m.
What is the range of a projectile on level ground?
R = 2v_x0 v_y0 / g, with v_x0 = v₀ cos θ and v_y0 = v₀ sin θ, for launch and landing at the same height.

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