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A particle is moving along the x-axis wi...

A particle is moving along the x-axis with an acceleration a = 2x where a is in `ms^(–2) and x` is in metre. If the particle starts from rest at x=1 m, find its velocity when it reaches the position x = 3.

A

8 m/s

B

16 m/s

C

4 m/s

D

0 m/s

Text Solution

AI Generated Solution

To solve the problem step by step, we will use the relationship between acceleration, velocity, and displacement. ### Step 1: Understand the relationship between acceleration, velocity, and displacement Given that the acceleration \( a \) is defined as: \[ a = \frac{dv}{dt} = 2x \] We can rewrite this using the chain rule: \[ a = \frac{dv}{dx} \cdot \frac{dx}{dt} = v \frac{dv}{dx} \] Thus, we have: ...
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Knowledge Check

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