the position of a bicyclist on a straight road in kilometers over a period of 4
ID: 2850009 • Letter: T
Question
the position of a bicyclist on a straight road in kilometers over a period of 4 hours is given by the graph in Figure 17, where inflection points occur when t=0.5 and t=2.
a) describe the motion of the bicyclist
6. The position of a bicyclist on a straigh eriod of 4 h is given by the graph in Figure 17. cur when r = 0.5 and 1-2. a) Describe the motion of the bicyclist ) Explain what the concavity of the graph over various interval s about the speed of the bicyclist. 30 25 05 1 2 3 4 FIGURE 17 7· The growth of a sunflower during the first 100 d r sprouting is modeled well by the logistic curve y ht) sho gure 18. Estimate the growth rate at the point of inflection a ain its significance. Then make a rough sketch of the first and erivatives of h. Height (cm)Explanation / Answer
a)from t =0 to 1 hours bicyclist moves in forward direction reaches 25 km from initial position and from t =1 to 3hours he reverses his direction travels 10 km and reaches 15 km from initial position, again from t =3 to 4hoursbicyclist moves in forward direction reaches 30 km from initial position
b)from t =0 to 0.5hours bicyclist moves in forward direction with increasing speed,from t =0.5 to 1hours moves in forward direction with decreasing speed and speed equals zero at t=1.from t =1 to 2hours bicyclist moves in reverse direction with increasing speed,from t =2 to 3hours moves in reverse direction with decreasing speed and speed equals zero at t=3,from t =3 to 4hours bicyclist moves in forward direction with increasing speed and reaches 30 km in 4 hours
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