# Find the acceleration, velocity and position

• MaxManus
In summary, the conversation discusses the motion of a sprinter with a mass of 80 kg, accelerated by a constant horizontal force of 400 N. The air resistance is taken into account using the equation 0.5*p*Cd*A*(v-w)**2, where p = 1.293 kg/m**3, Cd = 1.2, A = 0.45 m**2, and v and w represent velocity and wind speed respectively. The goal is to find the acceleration, velocity, and position of the sprinter. The solution involves using initial acceleration conditions and differential equations to solve for a logarithmic function of velocity with time, and then using the same method to obtain a function for position as a function
MaxManus

## Homework Statement

The motion of a sprinter with
mass = 80 Kg
the sprinter is accelerated with a constant horizontal force: 400 N
The air resistance is 0.5*p*Cd*A*(v-w)**2
p = 1.293 kg/m**3
Cd = 1.2
A = 0.45 m**2
v = velocity
w = 0 m/s

find the acceleration, velocity and position

## The Attempt at a Solution

a1 = 400N/80kg

a(t) = a1*t - (1/m)*0.5*p*Cd*A*(v)**2

Can someone help me with the v?
I am allowed to solve it numerically

MaxManus said:

## Homework Statement

The motion of a sprinter with
mass = 80 Kg
the sprinter is accelerated with a constant horizontal force: 400 N
The air resistance is 0.5*p*Cd*A*(v-w)**2
p = 1.293 kg/m**3
Cd = 1.2
A = 0.45 m**2
v = velocity
w = 0 m/s

find the acceleration, velocity and position

## The Attempt at a Solution

a1 = 400N/80kg

a(t) = a1*t - (1/m)*0.5*p*Cd*A*(v)**2

What is the a1*t term supposed to represent?

Can someone help me with the v?
I am allowed to solve it numerically
I think this one can only be solved numerically. What have you been taught so far about that? There are many different ways to solve it numerically, it would be good if you can tell us what your professor or textbook says about this.

Solved, I will post my solution later.

Use initial acceleration condition and differential equations to solve the problem you geta logarithimic function of velocity with time..now again use same to get position as a function of time .

## 1. What is acceleration and how is it calculated?

Acceleration is the rate of change of an object's velocity over time. It is calculated by dividing the change in velocity by the change in time. This can be expressed as a formula: a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

## 2. How is velocity related to acceleration?

Velocity and acceleration are closely related, as acceleration is the change in velocity over time. This means that if an object's velocity is increasing, its acceleration is positive, and if its velocity is decreasing, its acceleration is negative.

## 3. What is the difference between average and instantaneous acceleration?

Average acceleration is the overall rate of change of an object's velocity over a given period of time. Instantaneous acceleration, on the other hand, is the acceleration at a specific moment in time. It is calculated by taking the limit as the time interval approaches 0 in the formula for average acceleration.

## 4. How can acceleration, velocity, and position be represented graphically?

Acceleration can be graphed as the slope of a velocity vs. time graph, which shows the change in velocity over time. Velocity can be graphed as the slope of a position vs. time graph, which shows the change in position over time. Position can be graphed as a function of time, showing the object's displacement over time.

## 5. How can acceleration, velocity, and position be calculated using calculus?

Acceleration can be calculated by taking the derivative of the velocity function with respect to time. Velocity can be calculated by taking the derivative of the position function with respect to time. And position can be calculated by taking the integral of the velocity function with respect to time.

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