The origin is on flat ground, and the z-axis points upward. for time 0 ≤ t ≤ 10, a particle moves along a path given by ⃗r(t) = 2ti + 3tj + (100 − (t − 5)2 ) ⃗k. for what time(s) 0 ≤ t ≤ 10 is the particle at its highest point and what is its position then? for what time(s) 0 ≤ t ≤ 10 is the particle moving fastest? what is the fastest speed? for what time(s) 0 ≤ t ≤ 10 is the particle moving slowest? what is the slowest speed?

t= 5 s the particle will be on the highest position.

The maximum values of particle will at t= 10 s

The minimum values of particle will at t= 5 s

Explanation:

Given that

Time when the particle will be on the highest position:

  When the Z component of r(t) will be maximum then the particle will be on the highest position.

It means at t= 5 s the particle will be on the highest position.

Position at t= 5

Speed :

The maximum values of particle will at t= 10 s

The minimum values of particle will at t= 5 s

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