Can a vector with a non component be zero?

no. The magnitude of a vector is defined (or measured) as the square root of the sum of the squares of it's components. So, the magnitude will be 0 if and only if the “sum of the squares of it's components” is 0.

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what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2

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