Very small forces can have tremendous effects on the motions of every small object. an electron, mass 9.1 x 10 ^-31 kg, exerinces a force of 1.6 x 10^-17 n in a typical electric field at the earths surface. from rest, how much time would it take for the electron to reach the speed of 3.0 x 10^6 m/s?

t = 1.7 x 10⁻⁷ s

Explanation:

Given,

The mass of the electron, m = 9.1 x 10⁻³¹ Kg

The force experienced by the electron, F = 1.6 x 10⁻¹⁷ N

The initial velocity of the electron, u = 0

The final velocity of electron, v = 3.0 x 10⁶ m/s

The acceleration of the electron is given by the relation

                                         a = F/m

                                            = 1.6 x 10⁻¹⁷ N / 9.1 x 10⁻³¹ Kg

                                            = 1.76 x 10¹³ m/s²

Using the first equation of motion

                                        v = u + at

                                        t = (v - u) / a

                                          = (3.0 x 10⁶ - 0) /  1.76 x 10¹³

                                          = 1.7 x 10⁻⁷ s

Hence, the time taken by the electron to reach final speed is, t = 1.7 x 10⁻⁷ s

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