7 A particle of mass 0.8 kg is attached to one end of a light elastic string of natural length 2 m and modulus of elasticity 20 N . The other end of the string is attached to a fixed point \(O\). The particle is held at rest at \(O\) and then released. When the extension of the string is \(x \mathrm {~m}\), the particle is moving with speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- By considering energy show that \(v ^ { 2 } = 39.2 + 19.6 x - 12.5 x ^ { 2 }\).
- Hence find
(a) the maximum extension of the string,
(b) the maximum speed of the particle,
(c) the maximum magnitude of the acceleration of the particle.
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