A particle moves along the x-axis so that at time t≥0t\ge 0t≥0 its position is given by x(t)=−t3+6t2−9t+42.x(t)=-t^3+6t^2-9 t+42.x(t)=−t3+6t2−9t+42. Determine the total distance traveled by the particle from 0≤t≤4.0\le t \le 4.0≤t≤4.

4 units

Step-by-step explanation:

The given position function: , where t≥0.

To determine:  Total distance traveled by the particle from 0≤ t ≤ 4.0.

At t=0,

At, t=4,

Total distance traveled by the particle from 0≤ t ≤ 4.0 = |42-38| units

= 4 units

Hence, the distance traveled by the particle from 0≤t≤4.0 is 4 units.

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step-by-step explanation: