Observed from two frames S₁ and S₂ , the acceleration of a particle has an equal magnitude of 4 ext m/s ^2 .

Step-by-step solution

Let the acceleration of the particle with respect to frame S₁ be a _ p1 and with respect to frame S₂ be a _ p2 . Given | a _ p1 | = 4 m/s ^2 and | a _ p2 | = 4 m/s ^2 . The acceleration of frame S₂ with respect to frame S₁ is given by relative motion: a ₂₁ = a _ p1 - a _ p2 The magnitude of a ₂₁ is: | a ₂₁| = | a _ p1 |^2 + | a _ p2 |^2 - 2| a _ p1 || a _ p2 | where is the angle between the vectors a _ p1 and a _ p2 . Substituting the given magnitudes: | a ₂₁| = 4^2 + 4^2 - 2(4)(4) = 32(1 - ) Since the value of lie