Question

A cross-country runner follows a circular path that curves to his left. As he follows this path at constant speed. What is the direction of his acceleration when he is facing straight north?

• A. north
• B. south
• C. east
• D. west
• E. His acceleration is zero.

Answer 1

The correct option is D west

As the runner is at a constant speed , so he is doing uniform circular motion . No change in speed ,therefore magnitude of tangential acceleration is also zero .Now acceleration is only due to change in direction of velocity , and is given by ,

$\overrightarrow{a}=({\overrightarrow{v}}_2-{\overrightarrow{v}}_1)/t$ ,

above relation shows that direction of acceleration vector will be the direction of velocity change vector (resultant of ${\overrightarrow{v}}_2-{\overrightarrow{v}}_1$) , if we take two velocity vectors ${\overrightarrow{v}}_2,{\overrightarrow{v}}_1$ between a time interval of $t$ , we will find that the direction of ${\overrightarrow{v}}_2-{\overrightarrow{v}}_1$ is towards the center of circular path . It means direction acceleration $\overrightarrow{a}$ is also towards the center .

By using above reason , the direction will be towards west in the given case when runner is facing towards north .