Acceleration a is given as
a=dtdv⟹dv=adt⟹v=∫adt The function of the velocity (v) is given as:
v=∫4t−3/2dt=4∫t−3/2dt=4∫t231dt=4(−t2)v=−t8+c Velocity (v) is given as:
v=dtds⟹ds=vdt⟹s=∫vdt The function of the equation of motion can be obtained as follows:
s=∫(−t8+c)dt=−8(2t)+cts=−16t+ct+c1
When s = 16 and t = 4:
16=−16(4)+c(4)+c1=−16(2)+4c+c116=−32+4c+c1⟹4c+c1=48…(eqn1)
When s = 25 and t = 6:
25=−16(6)+c(6)+c1=−16(6)+6c+c125=−16(2.45)+6c+c16c+c1=25+39.2⟹6c+c1=64.2…(eqn2)
Solving eqn 1 and eqn 2 simultaneously:
4c+c1=48(−)6c+c1=64.2−−−−−−−−−−2c=−16.2c=8.1 Hence we find c1 :
4(8.1)+c1=4832.4+c1=48c1=48−32.4c1=15.6 Therefore, the equation of the motion s=f(t) is:
s=f(t)=−16t+8.1t+15.6
The velocity v(t) is:
v(t)=−t8+8.1
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