Differential equation dv/dt = 9.8 - v/5, v(0) = 0

[e^(i Pi)+1=0]

A falling object satisfies the initial value problem:

dv/dt = 9.8 - v/5, v(0) = 0

1.Find the time that must elapse for the object to reach 98% of its limiting velocity.

answer: t = 19.56, and for completeness, v = -49e^-t/5 + 49

2.How far does the object fall in the time found in part a?

Integrating yields the wrong answer, which should = 718.34?

p(t) = 245e^-t/5 + 49t

 

[SammyS]

A falling object satisfies the initial value problem:

dv/dt = 9.8 - v/5, v(0) = 0

1.Find the time that must elapse for the object to reach 98% of its limiting velocity.

answer: t = 19.56, and for completeness, v = -49e^-t/5 + 49

2.How far does the object fall in the time found in part a?

Integrating yields the wrong answer, which should = 718.34?

p(t) = 245e^-t/5 + 49t

What was it you integrated, and how did you do it?

 

[SithsNGiggles]

What was it you integrated, and how did you do it?

The p(t) at the bottom of the OP is suggests he/she integrated v(t) from part 1. Must be a problem with the limits of integration. I've gotten the right answer, and double-checked it.

 

[SammyS]

The p(t) at the bottom of the OP is suggests he/she integrated v(t) from part 1. Must be a problem with the limits of integration. I've gotten the right answer, and double-checked it.

Fair enough !

To OP:

What is p(19.56) - p(0) ?

 

[e^(i Pi)+1=0]

It was pointed out to me elsewhere that was how to do it. I did an indefinite integral and then evaluated p(19.56). I'm having a difficult time intuiting why that would yield a wrong answer though.

 

[SammyS]

It was pointed out to me elsewhere that was how to do it. I did an indefinite integral and then evaluated p(19.56). I'm having a difficult time intuiting why that would yield a wrong answer though.

Because for, p(t), as you have it, p(0) ≠ 0 . You could have used a constant of integration to make p(0) = 0 .