The force F, acting on an object is specified in newtons as a function of the sp

Question

The force F, acting on an object is specified in newtons as a function of the speed, v[m/s]: F (v ) = - 8v, How long does it take for the speed to drop down to 20% of its initial value? The mass for the object is 2 kg. Pick the closest answer in seconds.

0.4 is the correct answer, but how? Thanks ahead.

Q6 -The force F, acting on an object is specified in newtons as a function of the speed, wIm/sl F (v) -8v How long does it take for the speed to drop down to 20% of its initial value? The mass for the object is 2 kg. Pick the closest answer in seconds. (a) 1.3 (b) 0.8 (c) 1.6 (d) 0.05 (e) 0.40

Explanation / Answer

we know a = F/m

a = -8v/2 = -4v

a= dv/dt = -4v

dv/4v = -dt

0.25* lnv = -t

- 0.25 ln(20/100) = delta T

delta T = 0.40 s Answer

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