University Physics I · 1D Kinematics · 2.05
Constant-acceleration equations
Derivation and use of the standard relations, with initial conditions and applicability stated.
Build the model
Connect the measurement to the mechanism.
Derivation and use of the standard relations, with initial conditions and applicability stated. Treat this course-map statement as a claim to test rather than an invitation to import a familiar equation. In 1D Kinematics, begin from motion diagrams, then state the system, observable, assumptions, and evidence before calculating.
- Simple definition
- Derivation and use of the standard relations, with initial conditions and applicability stated.
- Example
- A strong response uses x–t, v–t, and a–t graphs and states where the model stops being reliable.
The velocity-time graph is a straight line of slope a.
a must be constant over the interval.
The area under the velocity-time graph gives displacement.
Choose and keep one signed axis.
The subsection's claim
Derivation and use of the standard relations, with initial conditions and applicability stated.
How to work with it
Start from motion diagrams. Then selecting a representation and connecting graph features to equations. Select an equation only after its variables and assumptions match the stated system.
What evidence would decide
When is a cart's acceleration adequately constant? Useful evidence includes position-time data, velocity estimates, model fit, residuals, and scale uncertainty.
Keep the boundary visible
This GioPhysics course map is an adaptable teaching sequence, not a claim of accreditation or a universal university syllabus. Departments can adjust the order, mathematical depth, laboratory hours, and optional fluids endpoint to match local requirements. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.
Change one variable at a time
Make the relationship visible.
Change u and a, then compare the endpoint velocity with the signed area under the graph.
FINAL VELOCITY8.00 m/s
DISPLACEMENT24.00 m
Live interpretationFINAL VELOCITY: 8.00 m/s. DISPLACEMENT: 24.00 m
Catch the common trap
Explain before calculating.
When may the constant-acceleration equations be used directly?
Choose an answer to test the model.
Practice & worked examples
Reason from the model, then test the result.
Worked calculationA cart starts at 4.0 m s⁻¹ and accelerates constantly at 3.0 m s⁻² for 5.0 s. Find its final velocity and displacement.
- v=u+at=4.0+(3.0)(5.0)=19 m s⁻¹.
- Δx=ut+½at²=(4.0)(5.0)+½(3.0)(5.0²).
- Δx=20+37.5=57.5 m.
AnswerThe final velocity is 19 m s⁻¹ and the displacement is 57.5 m.
TransferDesign one observation that separates Constant-acceleration equations from Free fall and vertical motion.
- Name the observable central to Constant-acceleration equations.
- Name the contrasting observable or condition in Free fall and vertical motion.
- Choose a graph feature, sign, scale, or limiting case that would distinguish them.
AnswerThe comparison is useful only if the proposed observation could rule out at least one of the two accounts.