The rear of a truck is open and a 20 kg box is 4 m from the open end. Coefficient of Friction between truck and block is μ = 0.15, the truck starts from rest with acceleration 2 m s⁻². How far does the truck move before the box falls off? Take g = 10 m s⁻².
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Question

The rear of a truck is open and a 20 kg box is 4 m from the open end. Coefficient of Friction between truck and block is μ = 0.15, the truck starts from rest with acceleration 2 m s⁻². How far does the truck move before the box falls off? Take g = 10 m s⁻².

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G1 Physics · Accepted Answer

The box can accelerate only due to friction, so its acceleration is μg = 1.5 m s⁻², while the truck accelerates at 2 m s⁻². Relative acceleration is 0.5 m s⁻². To move 4 m backward relative to the truck: 4 = ½(0.5)t², so t = 4 s. The truck moves ½(2)(4²) = 16 m.