Question

The displacement of a particle which moves along the s-axis is given by s = (t-3)exp(-0.6t)‚ where s is in meters and t is in seconds. Plot the displacement, velocity, and acceleration versus time for the first 20 seconds of motion. Determine the time at which the acceleration is zero?

Answer 1

Soft-3) e-0.67 At tzo -) S =-3 At t= f = S =-1.0976 At t22) Sa. 2-) So -0.3 At t = 3 ) S = Att zsz) Sz0.1 At tzlo S zo.0174 At tz 15 =) S = 0.0015. At tz202) S = D.ooo1044

-0.3 6.1 Sulst .o 6t e 0.60 e (4-3) (-0.63e obt Vee-oot -0.6t 0.6t Now. Va vist S = (t -3) Preds. dt [1 + (1 - 3) (-0.6) 0.611.91-067+18] o 6t [-0-67-1.27 (1.240.6t)e V [2.8 -0.67] At t 0 v= 2.8 Alt I ) V2 1. 201 At t.22 vzo.482 Att: 4.67 ) Vzo At t = 5 V At taloova -0.008 At t=15>) V2 -0.00076 At t = 200) V2 - 0.0000565 4 0.010 S

+ -0.61 Now v2.8 -0.6t 6476 a- dv 0.61 0.6e 0.61728-067 20-060 dt -0.6 e [-06-188+0.34+) Q: 62.28.70.36t)e-06 At t=0>) V-2:28 Attr] => Arr10s At t=2 a=-0.47 At t=8 => as-0.024 Att: 6:33) 0 0 Att =10) a=0.0033 At t = 20 => a = 0.00008 6.33 a -2.28 Now 060 2:{-228+0.3 6 t)e 06 A4 ao t Please 2:28+0.36t 6:3.3 seconds upvote if you Soln