The acceleration of a particle moving rectilinearly is a=4-2x, where x is in metre and a in m s⁻². It is instantaneously at rest at x=0. At what position x, in metre, will it again come to instantaneous rest?
Physics · Kinematics Part-1 (one dimension) · Acceleration and Avg acceleration
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Question

The acceleration of a particle moving rectilinearly is a=4-2x, where x is in metre and a in m s⁻². It is instantaneously at rest at x=0. At what position x, in metre, will it again come to instantaneous rest?

Physics · Kinematics Part-1 (one dimension) · Acceleration and Avg acceleration

G1 Physics · Accepted Answer

Use a=v dv/dx=4-2x. Starting from rest at x=0, v²/2=∫₀ˣ(4-2x)dx=4x-x². For the next rest point v=0, so 4x-x²=0 ⇒ x=4 m (non-zero root).