Help with Dynamics FE Examination Problem (Forces and Motion)?

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F-ma gives (*): 50e^t=550d²s/dt²=550dv/dt. Integrating gives
v=(1/11)e^t+C. When t=0, v=0, so C=-1/11→(**) v=(1/11)(e^t-1).
By (*) at t= 4, a=d²s/dt²=(1/11)e^4=4.96m/s².
By (**) v=4.873m/s.
v=ds/dt=(1/11)(e^t-1)→
s=(1/11)e^t-t/11+C'. When t=0, s=0→
C'=-1/11→s=(1/11)e^t-t/11-1/11→
s(4)=4.509m....Show more

CAREFUL.... F=ma ONLY IF acceleration is constant
otherwise its:
F=m*dv/dt

F*dt=m*dv
intigrate
50*e^t*dt
gives
50*e^t=m*v+C <---forgot +C first time around and its important
v=50/m*e^t+C
V at t=0 needs to be zero, since object starts at rest
V(0)=0=50/m*e^0+C
C=-50/m
v=50/m*(e^t-1)
a=dv/dt
a=50/m*e^t
v=ds/dt
or
ds=v*dt
s=50/m(e^t-t)+C <====once again forgot C the first try
S at t=0 also needs to be zero
s(0)=0=50/m(e^0-0)+C
C=-50/m
s=50/m*(e^t-t-1)

so you have
a=50/m*e^t
v=50/m*(e^t-1)
s=50/m*(e^t-t-1)

a(4)=50/550*e^4
v(4)=50/550*(e^4-1)
s(4)=50/550*(e^4-5)...Show more

force F= m * a

v^2=0^2 + 2*a*s

s=1/2 a*t^2...
hope everything's clear. :-)...Show more