A car starts from rest and accelerates to 30 mph. Later, it gets on a highway an

Question

A car starts from rest and accelerates to 30 mph. Later, it gets on a highway and accelerates to 60 mph. (The car weight is 5,000 kg.) Which takes more energy, the 0 to 30 mph, or the 30 to 60 mph? What the Kinetic energy change from 0 to 30 mph? What the Kinetic energy change from 30 to 60 mph? How much energy is required to stop the 60-mph car? The work accelerates a car from 0 to 50 km/hr is W_0. How much work is needed to accelerate the car from 50 km/hr to 150 km/hr? How much work is required to stop the 150-km hr car?

Explanation / Answer

m=5000kg, V2=48.2803m/s

a) E30-E0= 1/2*m*(V30^2-V0^2)=1/2*5000*(48.2803^2-0)=5827468.4J

E60-E30=1/2*5000*(96.5606^2-48.2803^2)=17482405.2607 This takes more energy

b)K.E Change E30-E0= 1/2*m*(V30^2-V0^2)=1/2*5000*(48.2803^2-0)=5827468.4J

c)E60-E30=1/2*5000*(96.5606^2-48.2803^2)=17482405.2607 J

d)E60-E0 = 1/2*5000*(96.5606^2-0)=23309873.6J

2) 50kmph=50*5/18=13.889m/s, 150kmph=41.667m/s

Work needed to accelerate from 0 to 50kmph =Wo=1/2*m*(13.889^2-0)=96.45*m

a) W50-150=1/2*m*(41.667^2-13.889^2)=771.62*m=771.62*Wo/96.45=8Wo (since m=Wo/96.45)

b)W150-W0 = 1/2*m*(41.667^2-0)=868.07*m=868.07*Wo/96.45=9*Wo

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