# Kinematics. Average Speed Problem Example

Here is the nice example of the average speed problem

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#### Timur

Created: 2023-12-18 07:07:34, Last updated: 2023-12-24 14:41:54

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Example: A car traveled half of the way at speed v1, the rest of the way it traveled half the time at speed v2, and the last section at speed v3. Find the average speed of the car along the entire way.

Solution:
By definition, average speed is the ratio of total path to total travel time. Hence we have:
$=\frac{s}{t}$
for the first half of the path
$\frac{s}{2}=v_1t_1$
for the second half
$\frac{s}{2}=v_2\frac{t_2}{2}+v_3\frac{t_2}{2}$

$t_1+t_2=t$
$v=\frac{s}{\frac{s}{2v_1}+\frac{s}{v_2+v_3}}=\frac{2v_1(v_2+v_3)}{v_2+v_3+2v_1}$

#### Kinematics. Average Speed Problem Example

Digits after the decimal point: 1
Average speed v (km/h)

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