Tyler and Jim race each other up a mountain on their bicycles. Tyler rides a road bike on the switchbacks of the twisting and turning mountain road. Jim rides a mountain bike and follows a direct, but steeper, straight-line path up the mountain. They start at the same time and place at the bottom of the mountain and finish at the same time and place at the top of the mountain. From start to finish a. whose distance traveled was longer? b. whose displacement was longer? c. which rider had the faster average speed? d. which rider had the faster average velocity? e. who won the race?

Explanation:

Displacement is minimum distance between initial and final point .

Distance is total length of path covered in a journey .

a )

Tyler covered a longer distance in the journey because total length of path covered by him is longer due to curved path .

b )

Both have same displacement , because minimum distance between initial and final point in both the case is same .

c )

average speed = distance / time

as time is same for both the case ,

average speed ∝ distance

As distance covered by Tyler is more , his average  speed is more .

d )

average velocity = displacement / time

As both displacement and time are same in both the case , average velocity in both the case is same .

e )

They start at the same time and place at the bottom of the mountain and finish at the same time , both have tie and nobody won the race , in spite of speed of Tyler being greater  .

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it would be c. predictability