Two horizontal forces act on a 2.5 kg chopping block that can slide over a frictionless kitchen counter, which lies in an xy plane. One force is `vec(F)_(1)=(3.0" N")hati+(4.0N)hatj`. Find the acceleration of the chopping block in unit-vector notation when the other force is (a) `vec(F)_(2)=(-3.0N)hati+(-4.0N)hatj`, (b) `vec(F)_(2)=(-3.0N)hati+(4.0N)hatj`, and (c) `vec(F)_(2)=(3.0N)hati+(-4.0N)hatj`.

Explanation

To solve the problem step by step, we will analyze the forces acting on the chopping block and calculate the acceleration for each case.

### Given:
- Mass of the chopping block, \( m = 2.5 \, \text{kg} \)
- Force \( \vec{F}_1 = (3.0 \, \text{N}) \hat{i} + (4.0 \, \text{N}) \hat{j} \)

### (a) When \( \vec{F}_2 = (-3.0 \, \text{N}) \hat{i} + (-4.0 \, \text{N}) \hat{j} \)

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