A cyclist rides 16.0 km east, then 8.0 km west, then 8.0 km east, then 32.0 km west, and finally

step 1 Question number 84. The first displacement is 16 kilometers towards east. Second displacement is

A cyclist rides 16.0 km east, then 8.0 km west, then 8.0 km...

A cyclist rides 16.0 km east, then $8.0 \mathrm{km}$ west, then $8.0 \mathrm{km}$ east, then $32.0 \mathrm{km}$ west, and finally $11.2 \mathrm{km}$ east. If his average velocity is $24 \mathrm{km} /$ h, how long did it take him to complete the trip? Is this a reasonable time?

Key Concepts

Time Calculation

Time calculation in kinematics often involves rearranging the average velocity formula. When the average velocity and net displacement are known, the time taken for the journey can be determined by dividing the net displacement by the average velocity.

Displacement

Displacement refers to the net change in position from the starting point to the ending point, taking into account the direction of travel. It is a vector quantity, meaning it has both magnitude and direction, and is found by summing up the individual movements with consideration for their directions.

Vector Addition

Vector addition is used to combine multiple displacement segments while keeping track of their direction. In problems involving east and west movements, distances in one direction are treated as positive and the opposite as negative, yielding a net displacement when summed.

Average Velocity

Average velocity is defined as the net displacement divided by the total time taken. It differs from average speed because it incorporates direction, meaning that opposing movements can cancel out, leaving a smaller net displacement even when the total distance traveled is large.

Reasonableness Check

Performing a reasonableness check involves verifying that the calculated time is consistent with the scale of the distances and speeds involved in the scenario. This step helps ensure that there are no calculation errors and that the result is realistic within the context of the problem.

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