How do I integrate acceleration function to get velocity?

Question

Noor Abdulrahman 2018-2-4

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回答： Alok Nimrani 2018-2-16

Hello everyone,

I'm trying to solve the following question using matlab.

A particle is fired vertically downwards with a velocity of 30 m/s in a fluid. Due to the resistance of the fluid, the particle experiences a deceleration equal to: a=-0.7v^3

if I want to obtain the velocity function I know I must integrate it using int(fun) but I'm not sure how to use it or how to set conditions.

I appreciate the help.

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Answer 1

Alok Nimrani 2018-2-16

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Hi Noor Abdulrahman,

Using the particle deceleration, a = dv/dt = -0.7(v^3), we have:

- dv/(0.7*v^3) = dt

Now, the initial velocity of the particle is 30 m/s i.e. v0 = 30 for t = 0. Assuming the velocity to be 'v' m/s at time instant 't', you can integrate:

left hand side of the above equation over the range 30 to 'v', and
right hand side of the equation over the range 0 to 't'

Please have a look at the following code for better understanding:

>> syms v t;                                                  % creating symbolic variables v and t
>> eqn = int(-1/(0.7*v^3), v, 30, v) == int(1, t, 0, t);  % 'eqn' represents the equation obtained after integrating both sides
>> solve(eqn, v)                                    % solving the above equation with respect to variable v

In this code, the ‘int(expr, var, lower, upper)’ function arguments are:

• Expression to integrate,

• Variable over which to integrate,

• Lower and upper limits of the integral

Hope this helps you.

Thanks