Acceleration a is given as
a=dtdvββΉdv=adtβΉv=β«adt The function of the velocity (v) is given as:
v=β«4tβ3/2dt=4β«tβ3/2dt=4β«t23β1βdt=4(βtβ2β)v=βtβ8β+c Velocity (v) is given as:
v=dtdsββΉds=vdtβΉs=β«vdt The function of the equation of motion can be obtained as follows:
s=β«(βtβ8β+c)dt=β8(2tβ)+cts=β16tβ+ct+c1β
When s = 16 and t = 4:
16=β16(4β)+c(4)+c1β=β16(2)+4c+c1β16=β32+4c+c1ββΉ4c+c1β=48β¦(eqn1)
When s = 25 and t = 6:
25=β16(6β)+c(6)+c1β=β16(6β)+6c+c1β25=β16(2.45)+6c+c1β6c+c1β=25+39.2βΉ6c+c1β=64.2β¦(eqn2)
Solving eqn 1 and eqn 2 simultaneously:
4c+c1β=48(β)6c+c1=64.2ββββββββββ2c=β16.2c=8.1 Hence we find c1β :
4(8.1)+c1β=4832.4+c1β=48c1β=48β32.4c1β=15.6 Therefore, the equation of the motion s=f(t) is:
s=f(t)=β16tβ+8.1t+15.6
The velocity v(t) is:
v(t)=βtβ8β+8.1
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