the acceleration of a particle traveling along a straight line is a = (0.02e^t)m

Question

the acceleration of a particle traveling along a straight line is a = (0.02e^t)m/s^2, where t is in seconds. If v=0, s=0 when t=0, determine the velocity and acceleration of the particle at s=4m.

Explanation / Answer

a = 0.02e^t dv/dt = 0.02e^t dv = 0.02e^tdt integrating both sides we get v = 0.02e^t + c at t =0 v=0 =>0 = 0.02 + c =>c = -0.02 so, v = 0.02e^t - 0.02 =>ds/dt = 0.02(e^t -1) =>ds = 0.02(e^t-1)dt integrating both sides we get s = 0.02(e^t -t) + d at t= 0 s =0 => 0 = 0.02 +d =>d = -0.02 so, s = 0.02(e^t - t -1) now s = 4 using iteration... t = 5.33s so, v = 0.02(e^5.33 -1) = 4.1m/s a = 0.02e^5.33 = 4.13m/s2.

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