- #1

NTesla

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- Homework Statement
- When we integrate velocity vector wrt time, we get displacement, and when we integrate magnitude of that velocity vector wrt time, we get distance. I've found this to be alright when a particle is in rectilinear motion. However, if the particle is moving in curved trajectory, is it still valid for calculation of displacement and distance ?

- Relevant Equations
- ##\int \vec{v}dt=Displacement##

##\int \left | \vec{v} \right |dt=Distance##

While solving question 1.13(see the attachment) from Irodov, I was doing this: $$\int_{0}^{\tau}(\vec{v}-ucos\theta) dt=l$$, and $$\int_{0}^{\tau}\vec{v}cos\theta dt=u\tau$$. Solving this gave the answer. However, while solving these 2 equations, I only used the

**magnitude**of ##\vec{v}##, and still got the displacement equal as is in RHS. But, if integrating speed wrt time should give distance, how are these 2 equations working to give correct answers?#### Attachments

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