i don't exactly know what they did there at t = 0 and x=24. Why didn't they just plugged the values in the integral like they did for t=6 and x = 96? Sorry if its not clear enough. My englissh is bad. I just dont know what they did there. Thank you in advance. PROBLEM 11.11The acceleration of a particle is directly proportional to the square of the time t. When t=0, the particle isat x = 24 m. Knowing that at t = 6 s, x=96 m and v=18 m/s, express x and v in terms of t.SOLUTIONWe haveNowAt t = 6 s, v=18 m/s:ororAlsoAt t=0, x= 24 m:orNowAt t = 6 s, x=96 m:orThenorandora=kt² k=constantdvdtSdv = "kt²dtv-18=k(t³ -=a=kt²dxdtv=18+k(f³-216)(m/s)==v=18+=k(t³ −23a = √[18+ 4(²-216)] dedxdtkx-24=18t+k1*-2161- 216)96-24=18(6)+(6)¹-216(6)3x-24=18t+x(t) =m/s41108v=18+v(t) =-216)39) = 2/7/²³ +10t-216t*+10t+24(t³-216)Solution Manual for "Vector Mechanics for Engineers -Dynamics," by F.P. Beer, E.R. Johnston, Jr., & P.J. Cornwell,Tenth Edition in SI Units, McGraw-Hill, 20136

The integral limits given are t=0, x=24m and t=6, x=96m

Answered: don't exactly know what they did there…

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i don't exactly know what they did there at t = 0 and x=24. Why didn't they just plugged the values in the integral like they did for t=6 and x = 96? Sorry if its not clear enough. My englissh is bad. I just dont know what they did there. Thank you in advance.

PROBLEM 11.11
The acceleration of a particle is directly proportional to the square of the time t. When t=0, the particle is
at x = 24 m. Knowing that at t = 6 s, x=96 m and v=18 m/s, express x and v in terms of t.
SOLUTION
We have
Now
At t = 6 s, v=18 m/s:
or
or
Also
At t=0, x= 24 m:
or
Now
At t = 6 s, x=96 m:
or
Then
or
and
or
a=kt² k=constant
dv
dt
Sdv = "kt²dt
v-18=k(t³ -
=a=kt²
dx
dt
v=18+k(f³-216)(m/s)
==v=18+=k(t³ −2
3
a = √[18+ 4(²-216)] de
dx
dt
k
x-24=18t+k1*-2161
- 216)
96-24=18(6)+(6)¹-216(6)
3
x-24=18t+
x(t) =
m/s4
1
108
v=18+
v(t) =
-216)
39
) = 2/7/²³ +10
t-216t
*+10t+24
(t³-216)
Solution Manual for "Vector Mechanics for Engineers -
Dynamics," by F.P. Beer, E.R. Johnston, Jr., & P.J. Cornwell,
Tenth Edition in SI Units, McGraw-Hill, 2013
6

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