Speed Physics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
A runner completes the first half of a race (5 km5 \text{ km}) at 10 km/h10 \text{ km/h} and the second half at 15 km/h15 \text{ km/h}. What is the runner's average speed for the entire race?

Solution

  1. 1
    Time for first half: t1=510=0.5 ht_1 = \frac{5}{10} = 0.5 \text{ h}.
  2. 2
    Time for second half: t2=515=13 ht_2 = \frac{5}{15} = \frac{1}{3} \text{ h}.
  3. 3
    Average speed = total distancetotal time=100.5+1/3=105/6=12 km/h\frac{\text{total distance}}{\text{total time}} = \frac{10}{0.5 + 1/3} = \frac{10}{5/6} = 12 \text{ km/h}.

Answer

vavg=12 km/hv_{\text{avg}} = 12 \text{ km/h}
Average speed is NOT the arithmetic mean of the two speeds (12.512.5). When distances are equal, average speed is the harmonic mean: 2v1v2v1+v2=2×10×1525=12\frac{2v_1 v_2}{v_1 + v_2} = \frac{2 \times 10 \times 15}{25} = 12.

About Speed

The rate at which an object covers distance over time, calculated as total distance divided by total time, always expressed as a non-negative scalar quantity.

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More Speed Examples

Example 1 easy

A jogger runs [formula] in [formula]. What is the average speed in m/s?

Example 2 easy

Light travels at [formula]. How far does light travel in [formula]?

Example 3 medium

A train travels [formula] at [formula] and then [formula] at [formula]. What is the average speed fo

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