8-A particle move along a curve so that dx/dt=sin(e^t/4)....

Question

8-A particle move along a curve so that dx/dt=sin(e^t/4) and dy/dt = (square root of the entire function t^2+5). Find the total distance traveled by the particle over the time interval 1 is less than or equal to t which is less than or equal to 3

Answer 1

Done in MATLAB

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% A particle move along a curve so that

% dx/dt=sin(e^t/4) and dy/dt = (square root of the entire function t^2+5)

% Find the total distance traveled by the particle over the

% time interval 1 is less than or equal to t which is less than or equal to 3

% Define time interval

% t:[1,3]

% In order to find the distance traveled by a particle

% you take the integral of the absolute value of the velocity function

% This means that the absolute value of the area under the curve of the velocity function

% equals the distance the particle travel

syms t

a=1

b=3

dx = sin(exp(t/4))

dy = sqrt(t^2 + 5)

% Distance Traveled = Integral(sqrt[ (dx)^2 + (dy)^2 ] dt ,a,b)

Distance_Traveled = int(sqrt( (dx)^2 + (dy)^2 ),t,a,b)

Numerical_Distance_Traveled=double(Distance_Traveled)

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Numerical_Distance_Traveled = 6.3703 meters

Best,

Maksim