3-A particle moves in the xy-plane...

Question

3- A particle moves in the xy-plane so that dx/dt=e^t/3 and dy/dt=cos(5t). What is the speed of the particle when t=2?

Answer 1

Done in MATLAB

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% A particle moves in the xy-plane

% dx/dt=e^t/3 and dy/dt=cos(5t)

% What is the speed of the particle when t=2?

% Define particle in 2D so let velocity = V < dx/dt , dy/dt>

syms t

time = 2

dx = exp(t/3)

dy = cos(5*t)

Vx_time= subs(dx,t,time)

Vy_time= subs(dy,t,time)

% Speed defined as magnitude( V(2) ) = ||( Vx_time Vy_time )||

V = [Vx_time Vy_time ]

Speed = sqrt(Vx_time^2 + Vy_time^2 )

Value_Speed = double(Speed)

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Output

time = 2

dx = e^t/3

dy = cos(5t)

Vx_time = e^2/3

Vy_time = cos(10)

V = <e^2/3 cos(10)>

Speed = [ e^4/3 + cos(10)^2 ]^0.5

Value_Speed = 2.1208 m/s

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Best,

Maksim