Problem Solving Strategies (Kinematics)
When solving a physics problem, first and foremost is to read the problem and then visualize it. Physics is advantageous in that most problems are based on situations you have experienced or observed and are capable of visualizing. Where is the object beginning its motion? Where does it end? Is there anything special about the motion? What path does it follow?
Here are some helpful strategies for particular types of problems and remember, focus on the methods and concepts, NOT on a specific type of problem.
Definitions (unit):
Kinematics: the branch of physics concerned with the mathematics of motion.
distance (m): total length of a path traveled, a scalar quantity, unit: m
displacement (m): the change of position of an object described by the vector that begins at the initial position of the object and ends at its final position.
speed (m/s): The time rate at which the distance traveled by a body increases with time; the magnitude of velocity in some cases (straight-line motion, instantaneous values); a scalar quantity
velocity (m/s): The time rate of change of displacement; a vector whose magnitude is speed and whose direction is the direction of motion.
average speed (m/s): the total distance traveled by an object divided by the time of its travel; a scalar quantity. In the case of uniformly accelerated motion, average speed is also the literal average of an objects initial and final speed.
acceleration (m/s2): The time rate of change of velocity; a vector quantity.
free-fall: motion solely under the influence of gravity. The acceleration of the object is 9.8 m/s2 straight down (near the surface of the Earth) whether the object is thrown upward, dropped, projected at an angle, or otherwise released.
Uniform motion:
Uniform motion means constant velocity (i.e. a = 0). The only equation applicable here is s = vt. The trip itself may include several parts, each of which is at a different speed (e.g. 3 hours at 40 km/h, then 30 minutes at 50 km/h), be careful, this case would still not be considered accelerated motion.
Uniformly Accelerated Motion (including free-fall):
1. READ the problem.
2. VISUALIZE or DRAW the situation.
3. What information is GIVEN?
4. What is problem asking for? What is NEEDED?
5. THINK! How are you going to approach the problem now? (this is usually the ‘time-consuming’ step… the more you practice the quicker this step becomes, hence the need for homework and problem drills)
6. Consider which EQUATION you will use. Is it APPLICABLE in this situation? (see uniform motion above)
7. CALCULATE.
8. Think about it, does your answer make SENSE?
9. Don’t forget UNITS!
Projectile Motion:
1. READ the problem.
2. VISUALIZE or DRAW the situation.
3. Analyze the HORIZONTAL and VERTICAL motions separately. If you are given an initial velocity and an angle, you may want to resolve it into x and y COMPONENTS.
4. Make a table of TWO COLUMNS for x values and y values.
5. What information is GIVEN? You know ay = +g or –g, where g = 9.8 m/s2, depending on whether you choose y positive up or down. Remember that vx never changes throughout and that vy = 0 at the highest point of any trajectory that returns downward.
6. What is problem asking for? What is NEEDED?
7. THINK! How are you going to approach the problem now? (this is usually the ‘time-consuming’ step… the more you practice the quicker this step becomes, hence the need for homework and problem drills)
8. Consider which EQUATION you will use. Is it APPLICABLE in this situation? (see uniform motion above)
9. CALCULATE. You may need to combine components of a vector to get a magnitude and a direction.
10. Think about it, does your answer make SENSE?
11. Don’t forget UNITS!
Adding Vectors:
1. DRAW a diagram (possibly on a set of axes), approximately to scale.
2. Resolve each vector into its x and y COMPONENTS. Remember the sign of each component is dictated by the QUADRANT the vector lies in. Also be careful that all angles are measured from the x-axis.
3. ADD the x-components together to get the x-component of the resultant. Same for the y components. You now have the components of the resultant vector.
4. If you need the magnitude of the resultant, use the PYTHAGOREAN THEOREM. If you need the angle, use the INVERSE TANGENT, but make sure the angle you write is in the appropriate QUADRANT. The angle must be written with some reference to where it is measured from (e.g. 40° S of W).
Relative Velocity:
1. READ the problem.
2. VISUALIZE or DRAW the situation.
3. What velocities are given? What SUBSCRIPTS will you use?
4. Write the VECTOR/SUBSCRIPT EQUATION. Remember the two "inner" subscripts must match and the two outer subscripts are the subscripts of the resultant vector.
5. DRAW the vector diagram based on your equation. The tip-to-tail method is appropriate here.
6. What is the problem asking for? What information do you need to find? From here, the problem usually becomes one of TRIGONOMETRY.