The accelerations of a particle as seen from two frames S₁ and S₂ have equal magnitude 4 m/s².
(a) The frames must be at rest with respect to each other.
(b) The frames may be moving with respect to each other.
(c) The acceleration of S₂ with respect to S₁ may either be zero of 8 m/s².
(d) The acceleration of S₂ with respect to S₁ may be anything between zero and 8 m/s².

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Solution

(d) The acceleration of S₂ with respect to S₁ may be anything between zero and 8 m/s².

Explanation:
${\vec{a}}_{s_{2} s_{1}} = {\vec{a}}_{s_{2} p} + {\vec{a}}_{p s_{1}} |{\vec{a}}_{s_{2} s_{1}}| = \sqrt{4^{2} + 4^{2} + 32 \cos (θ)}$
$- 1 < \cos (θ) < 1$
$0 < {\vec{a}}_{s_{2} s_{1}} < 8$

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(d) The acceleration of S2 with respect to S1 may be anything between zero and 8 m/s2. Explanation: a→s2s1=a→s2p+a→ps1a→s2s1=42+42+32cosθ -1<cosθ<1 0<a→s2s1<8

(d) The acceleration of S₂ with respect to S₁ may be anything between zero and 8 m/s².

Explanation:
${\vec{a}}_{s_{2} s_{1}} = {\vec{a}}_{s_{2} p} + {\vec{a}}_{p s_{1}} |{\vec{a}}_{s_{2} s_{1}}| = \sqrt{4^{2} + 4^{2} + 32 \cos (θ)}$
$- 1 < \cos (θ) < 1$
$0 < {\vec{a}}_{s_{2} s_{1}} < 8$