Complete COSMOS: Online Solutions Manual Organization System
Chapter 11, Solution 15.
Given: Separate variables Integrate using dv = kt2 dt v = 10 m/s when t = 0 and v = 10 m/s when t = 2 s. a= dv = kt 2 dt
10 22 10 dv = 0 kt dt
v
10 10
=
13 kt 3 1
t
0
[(10) (10)] = 3 k ( 2 )3 0
(a) (b) Solving for k, Equations of motion. k=
( 3)( 20 )
8
k = 7.5 m/s 4
Using upper limit of v at t, v
v 10
1 = kt 3 3
t
0
1 v + 10 = ( 7.5 ) t 3 3
v = 10 + 2.5 t 3 m/s Then, dx = v = 10 + t 2.5 3 dt dx = 10 + 2.5 t 3 dt
Separate variables and integrate using x = 0 when t = 2 s.
(
x dx 0
= 10 + 2.5 t 3 dt
t 2
t 2
(
)
)
x 0 = 10 t + 0.625 t 4
4 = 10 t + 0.0625 t ( 10 )( 2 ) + ( 0.625 )( 2 ) 4
= 10 t + 0.625 t 4 [ 10] x = 10 10t + 0.625t 4 m
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.