(a) Explanation Given information: The car A is traveling at the speed ( v A ) 0 40 mi/h when it enters a speed ( v A ) 30 mi/h zone. The driver of car A decelerates ( − a A ) at rate of − 16 ft/s 2 . The distance ( x A / B ) 0 between car A and car B is 60 ft . The constant speed ( v B ) 0 of car B is 45 mi/h . The driver of car B decelerates ( − a B ) at rate of − 20 ft/s 2 until reaching a speed ( v B ) of 28 mi/h . Calculation: Consider ( v A ) 0 : Convert the miles per hour to feet per sec. ( v A ) 0 = 40 mi/h × 1.46667 ft/s 1 mi/h = 58.667 ft/s Consider ( v A ) : Convert the miles per hour to feet per sec. v A = 30 mi/h × 1.46667 ft/s 1 mi/h = 44 ft/s Consider ( v B ) 0 : Convert the miles per hour to feet per sec. ( v B ) 0 = 45 mi/h × 1.46667 ft/s 1 mi/h = 66 ft/s Consider ( v B ) : Convert the miles per hour to feet per sec. v B = 28 mi/h × 1.46667 ft/s 1 mi/h = 41.067 ft/s At time 0 sec the car A enters the speed zone with velocity 58.667 ft/s , at time ( t A ) car A reaches its final speed of 44 ft/s . At time 0 sec the speed of the car B is 66 ft/s , at time ( t B ) 1 car B enters the speed zone with velocity of 41.067 ft/s and at time ( t B ) 2 it reaches the final speed. At time ( t min ) the speed v A of car A is equal to speed car B v B . Show the v-t curve from car A and car B as in Figure (1). Calculate the time ( t A ) using the relation: − a A = v A − ( v A ) 0 t A Substitute 44 ft/s for v A , 58.667 ft/s for ( v A ) 0 and 16 ft/s 2 for ( − a A ) . − 16 = ( 44 − 58.667 ) t A t A = ( 44 − 58.667 ) − 16 t A = 0.91669 sec Calculate the time ( t B ) 1 using the relation: ( x A / B ) 0 = ( t B ) 1 ( v B ) 0 Substitute 66 ft/s for ( v B ) 0 and 60 ft for ( x A / B ) 0 . 60 = ( t B ) 1 × 41.067 ( t B ) 1 = 60 66 ( t B ) 1 = 0.909 sec Calculate the time ( t B ) 2 using the relation: − a B = v B − ( v B ) 0 ( t B ) 2 − ( t B ) 1 Substitute − 20 ft/s 2 for − a B , 41.067 ft/s for v B , 66 ft/s for ( v B ) 0 and 0.909 sec for ( t B ) 1 . − 20 = 41.067 − 66 ( t B ) 2 − 0.909 − 20 = − 24.933 ( t B ) 2 − 0.909 ( t B ) 2 = − 24 (b) To determine The time ( t ) at which car A is 70 ft in front of car B.

12th Edition

ISBN: 9781264095032

Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 11.3, Problem 11.76P

(a)

To determine

The closest that car B comes to car A (xA/B)min.

(b)

To determine

The time (t) at which car A is 70 ft in front of car B.

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Chapter 11.3, Problem 11.75P

Chapter 11.3, Problem 11.77P

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The closest that car B comes to car A ( x A / B ) min .

Solution Summary: The author calculates the distance between car A and car B by converting the miles per hour to feet per sec.