A particle is moving in xy-plane. At certain instant, the components of its velocity and acceleration are as follows vₓ = 3 m/s, vᵧ = 4 m/s, aₓ = 2 m/s² and aᵧ = 1 m/s². The rate of change of speed at this moment is
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Question

A particle is moving in xy-plane. At certain instant, the components of its velocity and acceleration are as follows vₓ = 3 m/s, vᵧ = 4 m/s, aₓ = 2 m/s² and aᵧ = 1 m/s². The rate of change of speed at this moment is

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G1 Physics · Accepted Answer

The rate of change of speed is the tangential component of acceleration: dv/dt = (v⃗·a⃗)/|v⃗|. Here v⃗·a⃗ = 3·2 + 4·1 = 10 and |v⃗| = 5. Therefore dv/dt = 2 m/s², option B.