The position x as a function of time of a particle that move

The position x as a function of time of a particle that moves along a straight line is given by: X(t) = (-3 + 4t)e^-0.4t ft The velocity v(r) of the particle is determined by the derivative of x(t) with respect to r, and the acceleration a(t) is determined by the derivative of v(r) with respect to r. Derive the expressions for the velocity and acceleration of the particle, and make plots of the position, velocity, and acceleration as functions of time for 0 lessthanorequalto t lessthanorequalto 20 s. Use the subplot command to make the three plots on the same page with the plot of the position on the top, the velocity in the middle, and the acceleration at the bottom. Label the axes appropriately with the correct units. Growth data of a sunflower plant is given in the following table The data can be modeled with a function in the form H = C/(1 +Ae^-Br) (logistic equation), where H is the height, C is a maximum value for H, A and B are constants, and t is the number of weeks. By using the method described in Section 8.2.2, and assuming that C = 254 cm, determine the constants A and B such that the function best fit the data. Use the function to estimate the height in week 6. In one figure, plot the function and the data points.

Solution

24)

%Start the script

t=0:0.01:20;

x= (-3+4*t).*exp (-0.4*t);

v= (5.2-1.6*t).*exp (-0.4*t);

a= (-3.68+0.64*t).*exp (-0.4*t);

Subplot (3, 1, 1)

Plot (t, x)

Xlabel (‘time (s)’)

Ylabel (‘position (ft)’)

Subplot (3, 1, 2)

Plot (t, v)

Xlabel (‘time (S)’)

Ylabel (‘velocity (ft/s)’)

Subplot (3, 1, 3)

Plot (t, a)

Xlabel (‘time (s)’)

Ylabel (‘acceleration fT /s2)’)