06Unit 1 Review
Consolidate your understanding of kinematics, Newton's laws, acceleration, and two-dimensional motion with mixed conceptual questions, calculation problems, and a student self-check.
Reviewing the full unit before moving on helps you identify gaps, reinforce connections between concepts, and build the confidence to tackle Unit 2.
How do the concepts of kinematics, forces, and two-dimensional motion work together to describe and predict the movement of any object in the physical world?
Unit 1 Summary — Motion and Forces
Unit 1 builds the foundation of classical mechanics. In Chapter 1 you learned what physics is and how scientists use measurement, significant figures, and dimensional analysis. Chapter 2 introduced kinematics in one dimension — position, displacement, velocity, and the three big kinematics equations for constant acceleration. Chapter 3 deepened that understanding through acceleration and motion graphs: the slope of a position-time graph gives velocity, the slope of a velocity-time graph gives acceleration, and the area under a v-t graph gives displacement. Chapter 4 shifted from description to cause: Newton's three laws of motion, free-body diagrams, net force, and friction. Finally, Chapter 5 extended kinematics into two dimensions — vectors, projectile motion, and the independence of horizontal and vertical motion. Together these five chapters give you every tool needed to analyze any object moving under constant forces.
Key Equations
Worked Examples
A car starts from rest and accelerates uniformly at 3.0 m/s² for 8.0 s. How far does it travel?
Known: v₀ = 0, a = 3.0 m/s², t = 8.0 s
Use: x = v₀t + ½at²
x = (0)(8.0) + ½(3.0)(8.0)²
x = 0 + ½(3.0)(64)
x = 96 m
A velocity-time graph shows v = 12 m/s at t = 0 and v = −4 m/s at t = 4 s. What is the acceleration, and what does the sign tell you?
a = Δv / Δt = (v_f − v_i) / (t_f − t_i)
a = (−4 − 12) / (4 − 0)
a = −16 / 4
a = −4 m/s²
Negative sign → acceleration is opposite to the initial direction of motion (object is slowing down).
A 12 kg box is pushed along a frictionless floor by a horizontal net force of 36 N. What is its acceleration?
Known: ΣF = 36 N, m = 12 kg
Newton's 2nd Law: ΣF = ma → a = ΣF / m
a = 36 / 12
a = 3.0 m/s²
A 20 kg crate is pulled at constant velocity across a floor by a horizontal force of 50 N. Find the coefficient of kinetic friction.
Constant velocity → ΣF = 0, so applied force = friction force.
f_k = 50 N
Normal force: N = mg = (20)(9.8) = 196 N
μ_k = f_k / N = 50 / 196
μ_k ≈ 0.26
A ball is launched horizontally at 15 m/s from a cliff 45 m high. How long does it take to hit the ground, and how far from the base of the cliff does it land?
Vertical (free fall): y = ½gt² → 45 = ½(9.8)t²
t² = 45 / 4.9 = 9.18 → t = 3.03 s
Horizontal (constant velocity): x = v₀x · t
x = 15 × 3.03 = 45.5 m
Guided Practice
A train traveling at 30 m/s brakes with a deceleration of 1.5 m/s². How long does it take to stop, and how far does it travel while stopping?
Hint: Use v = v₀ + at to find t (set v = 0), then use v² = v₀² + 2aΔx to find Δx.
A position-time graph shows a straight line with a negative slope. Describe the object's motion. What would the corresponding v-t graph look like?
Hint: Slope of x-t graph = velocity. A negative constant slope means constant negative velocity — the v-t graph is a horizontal line below the time axis.
A 5.0 kg block hangs from a rope attached to the ceiling. Draw the free-body diagram and find the tension in the rope.
Hint: The block is in equilibrium: ΣF = 0. The only forces are tension T (up) and weight W = mg (down). Set T = mg.
A 10 kg box sits on a surface with μ_s = 0.40. What minimum horizontal force is needed to start the box moving?
Hint: Maximum static friction: f_s = μ_s · N = μ_s · mg. The applied force must exceed this value.
A soccer ball is kicked at 20 m/s at an angle of 30° above the horizontal. Find the horizontal and vertical components of the initial velocity.
Hint: v₀x = v₀ cos θ and v₀y = v₀ sin θ. Use cos 30° ≈ 0.866 and sin 30° = 0.500.
Key Vocabulary
Kinematics
The branch of physics that describes motion — position, velocity, and acceleration — without considering the forces that cause it.
Example: Using x = v₀t + ½at² to find where a car will be after 5 s.
Displacement
The change in position of an object; a vector quantity with both magnitude and direction.
Example: Moving 10 m east then 6 m west gives a displacement of 4 m east.
Velocity
The rate of change of displacement with respect to time; a vector quantity (speed + direction).
Example: A car moving north at 25 m/s has velocity +25 m/s if north is positive.
Acceleration
The rate of change of velocity with respect to time; a vector quantity. Can indicate speeding up, slowing down, or changing direction.
Example: A ball dropped from rest gains 9.8 m/s of speed every second.
Inertia
The tendency of an object to resist changes in its state of motion. Quantified by mass.
Example: A bowling ball is harder to start moving than a tennis ball — it has more inertia.
Net Force
The vector sum of all forces acting on an object. Determines the object's acceleration via ΣF = ma.
Example: Two forces of 10 N right and 4 N left give a net force of 6 N right.
Friction
A contact force that opposes relative motion between surfaces. Kinetic friction acts during sliding; static friction prevents sliding.
Example: f_k = μ_k · N for a box sliding across a floor.
Projectile
An object launched into the air that moves under gravity alone (no air resistance). Horizontal and vertical motions are independent.
Example: A ball thrown horizontally off a table follows a parabolic path.
Workbook Check — Unit 1
Interactive Practice — 5 Questions
A car accelerates from 0 to 24 m/s in 6.0 s. What is its acceleration?
On a velocity-time graph, what does the area under the curve between two times represent?
According to Newton's 1st Law, a hockey puck sliding on frictionless ice will:
A 15 kg object experiences a net force of 45 N. What is its acceleration?
A projectile is launched horizontally. Which statement is true throughout its flight (ignoring air resistance)?