Distance Traveled Versus Displacement Magnitude

Question

A particle moves in the $xy$-plane with a velocity vector given by $$\vec{v}(t) = \langle e^t, te^t \rangle$$. At time $t=0$, the particle is at the origin. What is the difference between the total distance traveled by the particle and the magnitude of its displacement from $t=0$ to $t=1$?

Accepted Answer

$$\int_0^1 e^t\sqrt{1+t^2}\,dt - \sqrt{(e-1)^2+1}$$

Answer

0

Answer

$$e - 1$$

Answer

$$e\sqrt{2} - \sqrt{2}$$

Distance Traveled Versus Displacement Magnitude

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