Kevin S. Huang

2015: Problem 2

Topic: Kinematics
Concepts: Average vs. instantaneous

Solution:

The average speed $v$ is

v=\frac{d}{t}

where $d$ is the distance traveled and $t$ is the time taken. We are given that the car travels at speed $v_1$ for distance $d_1$ in the first part of the journey and at $v_2$ for $d_2$ in the second part of the journey. The total distance is

d=d_1+d_2

The time for the first part is $t_1=d_1/v_1$ . The time for the second part is $t_2=d_2/v_2$ . Thus, the total time is

t=t_1+t_2=\frac{d_1}{v_1}+\frac{d_2}{v_2}

Putting everything together,

v=\frac{d_1+d_2}{\frac{d_1}{v_1}+\frac{d_2}{v_2}}=\frac{25+75}{\frac{25}{80}+\frac{75}{50}}\,\mathrm{km/hr}=55.2\,\mathrm{km/hr}

so the answer is A.

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Kevin S. Huang

2015: Problem 2

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2015: Problem 2

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