A proton moves in an electric field such that its acceleration a is a=-20 (1+2t) ^-2, where t is the time in seconds. Find the velocity as a function of time if v sub zero = 30 when t=0

A = dv/dt, therefore, to get an expression for v (t), we would integrate the expression for a:

a = - 20 / (1+2t) ^2

v = (1/2) * 20 / (1+2t) + k = 10 / (1+2t) + k

At t = 0:

v0 = 10/1 + k = 30

Therefore, k = 20, and the expression for v (t) is

v (t) = 10 / (1+2t) + 20