Starting from rest, a bicyclist travels around a horizontal circular path, r = 10 m, at a speed of v = (0.09t2 + 0.1t) m>s, where t is in seconds. Determine the magnitudes of his velocity and acceleration when he has traveled s = 3 m.

Explanation:

The position of the car at any instant is defined from the fixed point. The velocity and acceleration are to be determined at a point B (i.e s=3) . So, the origin of the n,t axes at this point (Check diagram)

Velocity:

The bicyclist travels around a horizontal circular path at a speed of v = (0.09t2 + 0.1t) m/s then the rate of increase in speed is

v= (0.18t-F 0.1) m/s2 (1)  

The time needed for the bicycle to reach point B can be determined by realising that the position of B is sb = 3 m and since sA = 0 when t = 0 we have  

v = ds/dt= (0.09t2 + 0.1t)) m/s (2)  

=

3 m= 0.03B + 0.05tB

tB= 4.15 s  

Substituting into Eq. 2 yields

vg = (0.09(4.15)2+0.1(4.15)) m/s  

= 1.965 m/s

Acceleration:

The tangential component of acceleration at B is obtained by substituting tb= 4.15 s into Eq. 1

(ab)n  = B / p = (0.18(4.15+ 0.1 )m/s² = 0.847 m/s²

Realising that the circular path is of radius p=10 m and using vb=1.985 m/s the normal component of acceleration at B is therefore

(ab)n = B / p = (1.965 m/s )² / 10m = 0.386 m/s²

The magnitude of acceleration is therefore given by

ab = => = 0.93

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water

more than, less

less than, more