The acceleration of a particle traveling along a straight line is a = (0.02e t )

Question

The acceleration of a particle traveling along a straight line is a = (0.02et)m/s2, where t is in seconds. If v=0, s=0 when t=0, determine the velocity and acceleration of the particle at s=4m.

a = 0.02et
dv/dt = 0.02et
dv = 0.02et dt
integrating both sides we get
v = 0.02et + c
at t =0 v=0
=>0 = 0.02 + c
=>c = -0.02

so, v = 0.02et - 0.02
=>ds/dt = 0.02(et -1)
=>ds = 0.02(et-1)dt
integrating both sides we get
s = 0.02(et-t) + d
at t= 0 s =0
=> 0 = 0.02 +d
=>d = -0.02

so, s = 0.02(et - t -1) *s=4m

4=0.02(et-t-1)

(et-t-1)=200

This is where Im stuck...how do I solve for t here? Dont just need the name of the method, but the actual method worked out. Once I solve for t I know how to solve for the velocity & acceleration.

Explanation / Answer

Use any online graph plotter and plot the function e^x-x-201 .The polynomial cuts x axis at x= 5.325 .There is no way other than graph plotter.

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