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

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.

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)

force F= m * a

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

s=1/2 a*t^2...

hope everything's clear. :-)