write an equation?

Question

A small positively charged object is placed, at rest, in a uniform electric field in vacuum. Write an equation giving its speed after a time t in terms of its mass m and charge q.

Answer 1

From Coulombs Law we know the force acting on the charged particle is,
F = E * q
Where F is the force, E is the electric field, and q is the charge.

From Newton's 2nd law we know that a force causes a mass to accelerate,
F = ma
a = F / m
Where F is the force, m is the mass, and a is the resulting acceleration.

The Coulomb force the charged particle experiences causes it to accelerate.
Since the electric field is uniform, the resulting force will be constant and thus cause a constant acceleration.

A change in velocity can be found as,
(delta v) = a * t
Where (delta v) is the change in velocity, a is the acceleration and t is the time.
Since the object starts from rest, its velocity at any given time is equal to its change in velocity from its initial, stationary, condition.

All we need to do now is combine the things we know into the single equation the problem asked for.

F = E * q = m * a = m * v / t,
Solving for v,
v = E * q * t / m

The objects velocity as a function of time (t) is given as,
Velocity = Electric field * charge * time / mass