If a car shifts gears from first to second after 5 seconds, whenthe speed is 60m

Question

If a car shifts gears from first to second after 5 seconds, whenthe speed is 60mph. Second to third happens after 10 secondswhen the speed is 85 mph. Its speed is 110 after 15seconds.

A). Find the time taken to complete .25 miles from rest.
B). Find the instantaneous velocity at the 5 second mark?
C).What is the Average velocity during the first 5 seconds?
D).What is the average acceleration during the first 10seconds?
E). At what time is the instantaneous acceleration equal to theacceleration found in D?

Explanation / Answer

Im going to assume that the car started at v=0 a) first phase, car travells (0+60mph)/2*5sec * 1hour/3600sec =0.041667 miles second phase, car travells (85+60mph)/2*10sec * 1hr/3600sec =0.2013888 miles (=0.243 miles total) happens during 3rd phase d=vot+1/2*a*t2, a= (110-85mph)/(15sec*1/3600) =6000mph/hour .25-.243=85*t+1/2*6000*t2 t=0.000082hr or 0.2952 sec, so total time = (0.2952+5+10) =15.2952 sec b)in the question, it says at 5 sec, velocity is60mph c) avg velocity during first 5 sec, a=(v2-v1)/2,a=(60-0)/(5sec*1/3600) = 43200mph/hour d)avg acceleration = total velocity/total time at 10 sec, v=(85+60)/2 = 72.5mph a=72.5mph/(10sec *1/3600) = 21600mph/hr e) there are 3 distinct instantaneous accelerations, they occurduring the 3 phases at no time will the instantaneous acceleration equal that in d

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