A particle moves as x = t²(t−2)². At the two positive instants at which its velocity is zero, let the accelerations be a₁ and a₂. The product a₁a₂ is:
Physics · Kinematics Part-1 (one dimension) · Acceleration and Avg acceleration
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Question

A particle moves as x = t²(t−2)². At the two positive instants at which its velocity is zero, let the accelerations be a₁ and a₂. The product a₁a₂ is:

G1 Physics · Accepted Answer

x = t⁴ − 4t³ + 4t². v = 4t³ − 12t² + 8t = 4t(t−1)(t−2). The positive instants are t=1 s and t=2 s. a = 12t² − 24t + 8. a₁ = a(1)=−4 m s⁻², a₂ = a(2)=+8 m s⁻². Therefore a₁a₂ = (−4)(8)=−32 m² s⁻⁴.