Find the magnitude of the force needed to accelerate a 280 g mass with a⃗ = -0.170 m/s2 i^+0.450 m/s2 j^.

Force = ma

Mass, m = 280g = 280/1000 = 0.28kg.

a = (-0.170i + 0.45j) m/s²

Since this is in vector form, let us find the magnitude of the acceleration.

a = √((-0.17)² + 0.45²). This is the formula for the magnitude using the vector components.

a = √(0.2314) ≈ 0.4810 m/s²

F = ma = 0.28 * 0.481≈ 0.13468

The force is ≈ 0.1349 N

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Newton's first law describes something special that results from the sum of all the external forces (including gravity) on an object.