Find the acceleration, velocity and position

[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

 

[Redbelly98]

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.

 

[MaxManus]

Solved, I will post my solution later.

 

[abhi@maths]

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 .