How much force is required to accelerate a 0.10 gram mosquito at 20m/?

 0.002 newtons

Work Shown:

I'm assuming you meant to write "at 20 m/s^2" at the end. If so, then,

0.10 grams = 0.10/1000 = 0.0001 kg

m = 0.0001 kg = mass

a = 20 m/s^2 = acceleration

F = ma newton's second law

F = 0.0001*20

F = 0.002

The force required is 0.002 newtons

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