A particle moves along the x-axis such that its position at time t is given by x = 2t^3 - 6t^2 + 4t. Find the total distance traveled by the particle in the interval t = 0 to t = 3 seconds.

C. 12 units — The velocity is v = 6t^2 - 12t + 4. Setting v = 0 gives t = 1 +/- 1/sqrt(3), so the particle changes direction. Calculate the displacement in each interval and sum the absolute values.

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$A particle moves along the x-axis such that its position at time t is given by x (t) = 2 t^{3} - 6 t^{2} + 4 t . Find the total distance traveled by the particle in the interval t = 0 to t = 3 seconds.$

A. $8 units$
B. $10 units$
C. $12 units$
D. $14 units$

Show correct answer & step-by-step solution

Correct answer: C — $12 units$

Solution

The velocity is v (t) = \frac{d x}{d t} = 6 t^{2} - 12 t + 4 . Setting v (t) = 0 gives t = 1 \pm \frac{1}{3} . Calculate the position at t = 0, 1 - 1/ 3, 1 + 1/ 3, and t = 3 to find the total path length.

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A particle moves along the x-axis such that its position at time t is given by x(t)=2t3−6t2+4t. Find the total distance traveled by the particle in the interval t=0 to t=3 seconds.

Solution

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More Kinematics practice questions

$A particle moves along the x-axis such that its position at time t is given by x (t) = 2 t^{3} - 6 t^{2} + 4 t . Find the total distance traveled by the particle in the interval t = 0 to t = 3 seconds.$