Study guide: Kinematics and Force Models
Analyze changes of motion using signed quantities and stated assumptions.
Ideas to explain in your own words
- Acceleration equals final velocity minus initial velocity, divided by elapsed seconds. Use the stated coordinate direction.
- Net force equals mass in kilograms multiplied by signed acceleration in meters per second squared. Keep acceleration’s sign.
- Displacement equals initial velocity times seconds plus one-half acceleration times seconds squared. Constant acceleration is an explicit assumption.
- A free-body diagram lists forces acting on one chosen body. An action-reaction partner acts on another body and should not be added as if both act on the same object.
Useful vocabulary
- m/s²
- Meters per second squared expresses acceleration: velocity change per time.
- Acceleration
- Acceleration equals final velocity minus initial velocity, divided by elapsed seconds.
- N
- Newton is the SI force unit, equal to one kilogram-meter per second squared.
- Net force
- Net force equals mass in kilograms multiplied by signed acceleration in meters per second squared.
- m
- Meter is the SI length unit; a displacement also needs its reference and direction.
- Displacement
- Displacement equals initial velocity times seconds plus one-half acceleration times seconds squared.
- chosen body
- object whose motion is analyzed
Watch your reasoning
- Using the distractor operation (a+b)/c instead of (a-b)/c; Keep final minus initial order.
- Using the distractor operation a+b instead of a*b; Use net force rather than a single force when others act.
- Using the distractor operation a*c+b*c instead of a*c+0.5*b*c*c; Square the time in the acceleration term.
A worked review example
Worked distinct example: A distinct model changes from 2 to 8 m/s in 3 s: (8-2)/3=2 m/s². Method: identify the quantities in the stated rule, substitute using compatible units, and perform the operations in the correct order. Keep final minus initial order. Acceleration can be negative while speed increases in a negative direction. Interpret the final unit and keep the model assumption visible; this calculation is not a measurement of a real learner or site. Worked distinct example: A distinct model has 3 kg mass and -2 m/s² acceleration: 3×(-2)=-6 N. Method: identify the quantities in the stated rule, substitute using compatible units, and perform the operations in the correct order. Use net force rather than a single force when others act. A newton is kg·m/s². Interpret the final unit and keep the model assumption visible; this calculation is not a measurement of a real learner or site. Worked distinct example: A distinct model has initial 1 m/s, acceleration 2 m/s² and time 2 s: 1×2+0.5×2×4=6 m. Method: identify the quantities in the stated rule, substitute using compatible units, and perform the operations in the correct order. Square the time in the acceleration term. Use displacement, not automatically path length. Interpret the final unit and keep the model assumption visible; this calculation is not a measurement of a real learner or site. Worked supplied problem: A floor pushes up on a cart, and the cart pushes down on the floor. Explain why these do not cancel on the cart’s free-body diagram. Solution: The two forces act on different bodies. The cart diagram includes the floor’s upward force and other forces on the cart, not the cart’s force on the floor. Net force must sum one body’s forces. This conclusion uses the stated observations and the mechanism explained above; it does not establish every unmeasured feature of a real organism, device or place.
Make a practice plan
- Explain the mechanism in Calculate constant acceleration using a labeled case.
- Complete Use a net-force model and correct the specific misconception in its feedback.
- Resolve a changed case from Predict constant-acceleration displacement, then combine the four ideas in the transfer task.