Find the initial velocity of a particle given its constant acceleration and its displacement over a specific time interval.

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Finding Initial Velocity from Constant Acceleration and Displacement

Rectilinear and curvilinear motion warmup

A particle moving along a straight line is accelerating at the constant rate of \( 3 \text{ m/s}^2 \). Find the initial velocity \( v_0 \), if the displacement during the first two seconds is \( 10 \text{ m} \).

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What you need first

Basic integration (power rule)
Understanding of position, velocity, and acceleration
Solving linear equations

What this problem tests

Tests the ability to integrate acceleration to find velocity and position, and to apply initial conditions and displacement definitions to solve for an unknown constant.

This is a standard introductory kinematics problem found in Calculus I and introductory physics courses.

Finding Initial Velocity from Constant Acceleration and Displacement

What you need first

What this problem tests

More on Rectilinear and curvilinear motion