Speed, Time, and Distance

Flashcards reviewing key concepts and formulas related to speed, time, and distance problems.

Speed

A measure of how quickly an object moves from one place to another, calculated as distance traveled divided by the time of travel.

Formula for Speed (r)

Distance (d) / Time (t)

Formula for Time (t)

Distance (d) / Speed (r)

Formula for Distance (d)

Speed (r) × Time (t)

Consistency of Units

Ensuring that the units of distance, time, and speed are compatible (e.g., meters/second and seconds, or miles/hour and hours).

Inconsistency of Units

Often occurs between speed and time. Convert time to hours if speed is in mph, or to seconds if speed is in meters per second.

Multiple Segments of Travel

A travel with more than one segment, each with a different speed. Drawing a picture depicting all segments helps in solving.

Multiple Objects in Motion

When more than one object is moving at different speeds in the same or opposite directions. Drawing a picture is helpful.

Setting up Algebraic Equations

Necessary to solve for unknown quantities in multi-segment/object problems. Requires at least one constant term.

Average Speed

The ratio of the total distance traveled to the total travel time.

Average Speed Formula

Total distance travelled / Total travel time = (d1+d2) / (t1+t2), where t1 = d1/r1 and t2 = d2/r2

Common Mistake in Calculating Average Speed

Incorrectly calculating average speed as (r1 + r2)/2, which is only valid if t1 = t2.

Two Objects Moving in Same/Opposite Directions (Same Spot)

Problems involving two objects starting from the same point but possibly at different times.

Two Objects Moving in Opposite Directions Between Two Points

Problems where two objects start from two different points moving towards each other.

Key Concept for Objects Moving Towards Each Other

The total distance traveled by the two objects to the meeting point equals the distance between their starting points (d1 + d2).