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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.01 W01D3-1: Model Rocket Solution A person launches a home-built model rocket straight up into the air. At t = 0 the rocket is at rest at y = 0 with v y,0 = 0. The position of the rocket is given by a 1 y(t) = (a0 - g)t 2 - 0 4 t 6 ; 2 30t0 0 < t < t0 (1.1) where a0 is a positive constant and g is the acceleration of gravity. t0 is the time that the fuel burns out. Find the y -components of the velocity and acceleration as a function of time. Graph the y -component of the acceleration vs. time. Solution: We differentiate the position function to find an expression for the velocity v y (t) valid at all times in the interval 0 < t < t0 . v y (t) = a dy(t) = (a0 - g)t - 04 t 5 ; dt 5t0 0 < t < t0 (1.2) We now differentiate v y (t) to find an expression for the acceleration a y (t) valid at all times in the interval 0 < t < t0 . a y (t) = dv y (t) dt = (a0 - g) - a0 t0 4 t4; 0 < t < t0 (1.3) The graph below shows a plot of a y (t) vs. t for a choice of values a0 = 40 m × s-2 , g = 10 m × s-2 , and t0 = 2 s .