Question

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

Answer 1

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