Question
Asked Nov 9, 2019

Can i get help step by step with this problem?

24. Solve the initial value problem.
2 dr
h45, r(2)5
r(t)
help_outline

Image Transcriptionclose

24. Solve the initial value problem. 2 dr h45, r(2)5 r(t)

fullscreen
check_circle

Expert Answer

Step 1

From given second derivative find first derivative using integration.

Where , C=constant

d'r
2
dt2
dr
2
dt
dt
dr
2t dt
dt
-2
dr
-2
-2
-+C
dt
dr
-t -?+C\
dt
help_outline

Image Transcriptionclose

d'r 2 dt2 dr 2 dt dt dr 2t dt dt -2 dr -2 -2 -+C dt dr -t -?+C\ dt

fullscreen
Step 2

At t=4 , dr/dt=5

From there find C

C=5.0625

dr
=-t 2+C
dt
5=-(4)+C
C=5+(4)
C-5.0625
help_outline

Image Transcriptionclose

dr =-t 2+C dt 5=-(4)+C C=5+(4) C-5.0625

fullscreen
Step 3

From dr/dt find r using integration. K=constant

Given that at...

dr
=-t 2+5.0625
dt
r=f(-t 2+5.0625) dt
+5.0625t+K
-1
r=-
r=t+5.0625t+K
5=(2)5.0625(2)+K
K-5-(2)-5.0625(2)
K -5.625
help_outline

Image Transcriptionclose

dr =-t 2+5.0625 dt r=f(-t 2+5.0625) dt +5.0625t+K -1 r=- r=t+5.0625t+K 5=(2)5.0625(2)+K K-5-(2)-5.0625(2) K -5.625

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Other