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

• e^(i Pi)+1=0
In summary: Because for, p(t), as you have it, p(0) ≠ 0 . You could have used a constant of integration to make p(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

e^(i Pi)+1=0 said:
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?

SammyS said:
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.

SithsNGiggles said:
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) ?

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.

e^(i Pi)+1=0 said:
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 .

## 1. What is the meaning of the differential equation dv/dt = 9.8 - v/5?

The differential equation dv/dt = 9.8 - v/5 represents the rate of change of velocity (dv/dt) over time (t) for an object experiencing a constant acceleration of 9.8 m/s^2 and a drag force proportional to its velocity (v/5).

## 2. What does the initial condition v(0) = 0 signify?

The initial condition v(0) = 0 indicates that at time t = 0, the object has an initial velocity of 0 m/s. This could represent a stationary object or an object starting from rest.

## 3. How can this differential equation be solved?

This differential equation can be solved using separation of variables, where the variables are separated on either side of the equation and then integrated to find the general solution. The initial condition v(0) = 0 can then be used to find the specific solution.

## 4. What is the physical significance of the constant 9.8 in the equation?

The constant 9.8 represents the acceleration due to gravity on Earth. This means that in the absence of any other forces, an object will experience a constant acceleration of 9.8 m/s^2 towards the ground.

## 5. Can this differential equation be applied to real-world situations?

Yes, this differential equation can be applied to real-world situations involving objects experiencing a constant acceleration and a drag force proportional to their velocity. Examples could include objects falling through the air or vehicles driving at a constant speed against air resistance.

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