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
