Question
Why are mountain roads generally made winding upwards rather than going straight up?

Answer

On an inclined plane force of friction on a body going upward is $\text{f}_\text{s}=\mu\text{N}\cos\theta$ where $\theta$ is angle of inclination of a plane with horizontal if $\theta$ is small, the force of friction is high and there is a less chance of skidding.
The road straight up would have a larger angle and smaller would be the value of friction, hence more are the chances of skidding.

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