A cyclist rides 8.0 km east for 20 minutes, then he turns...

A cyclist rides $8.0 \mathrm{km}$ east for 20 minutes, then he turns and heads west for 8 minutes and $3.2 \mathrm{km}$. Finally, he rides east for $16 \mathrm{km},$ which takes 40 minutes. (a) What is the final displacement of the cyclist? (b) What is his average velocity?

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Key Concepts

Time Conversion

Accurate problem solving in kinematics often requires converting units of time into a consistent system, ensuring that time measurements (such as minutes or hours) align properly with displacement units when computing quantities like average velocity.

Vector Addition

In problems involving displacement with changes in direction, vector addition is used to combine different segments of the journey. This requires taking into account the direction of each segment, often by assigning positive and negative signs to movements along a single axis or by resolving them into components in multiple dimensions.

Displacement

Displacement is a vector quantity that represents the change in position of an object from its initial to its final location. It takes into account both the magnitude and the direction of movement, distinguishing it from distance, which only measures the total path length traveled.

Average Velocity

Average velocity is the rate at which an object's displacement changes over time. It is defined as the total displacement divided by the total time taken, and, like displacement, it has both magnitude and direction.

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