A vehicle travels on a road profile as shown. The driver applies full throttle to accelerate the
vehicle such that the horizontal component of the velocity v_(x)=10+0.15t(m)/(s). At time t=0,
the vehicle is at the position x=0 and y=0. Make the following plots for t=0 to 50s. Also
provide insights from your results. Do they match with the expected physics?
a) velocity versus time
b) the angle eta versus time
c) tangential acceleration versus time
d) normal acceleration versus time
e) instantaneous radius of curvature versus time.
In part (e), generate and compare two plots obtained by the following two formulas:
ho =(v^(2))/(a_(n)),
ho =([1+((dy)/(dx))^(2)]^((3)/(2)))/(|(d^(2)y)/(dx^(2))|)
A vehicle travels on a road profile as shown. The driver applies full throttle to accelerate the vehicle such that the horizontal component of the velocity vx = 10 + 0.15t m/s. At time t = 0, the vehicle is at the position x = 0 and y = 0. Make the following plots for t = 0 to 50 s. Also provide insights from your results. Do they match with the expected physics?
a) velocity versus time b) the angle versus time c) tangential acceleration versus time d) normal acceleration versus time e) instantaneous radius of curvature versus time
In part (e), generate and compare two plots obtained by the following two formulas:
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y = 0.0003x2
v=vet