Explanation Given: Points A and B are located 8 miles apart. Speed limit for first 5 miles is 60 mi/hr . Speed limit for last 3 miles is 35 mi/hr . Travel time between point A and B is 10 min 20 sec . Concept used: The car at point A starts from rest and accelerates at constant rate till its speed is 60 mi/hr and then travels with constant speed. Then, the driver decelerates before completing 5 miles froma speed of 35 mi/hr . After that the car travels at constant speed of 35 mi/hr and finally decelerates at the same rate till it completes 8 miles from the start. This can be plotted on the v − t plot as follows: Change in the displacement for the given v − t plot in theinterval is the area under the v − t graph for that duration. x f − x i = area under the v − t curve ...... (1) Here x f is the final displacement and x i is the initial displacement. Write the formula to calculate the acceleration from the data given in the graph. a = v 2 − v 1 t 2 − t 1 ...... (2) Where v 2 is final velocity and v 1 is initial velocity. The value of t 2 − t 1 is change in time. Let the magnitude of constant acceleration be a . For the interval A to D, the value of t 1 is as follows: a = 60 − 0 t 1 t 1 = 60 a For the interval E to C, the value of t 3 is as follows: a = 60 − 35 t 3 t 3 = 25 a Change in the displacement for the given v − t plot in the interval C to B is as follows: x C − x A = [ 1 2 ( t 1 ) ( 1 D ) ] + [ ( 1 D ) ( t 2 ) ] + [ 1 2 ( 3C+2E ) ( t 3 ) ] ...... (3) For the interval F to B, the value of t 5 is as follows: a = 35 − 0 t 5 t 5 = 35 a Change in the displacement for the given v − t plot in the interval A to C is as follows: x B − x C = ( 3 C ) ( t 4 ) + 1 2 ( t 5 ) ( 4 F ) ...... (4) The total time taken to complete 8 miles is 10 min 20 sec . Convert this into hours as follows: 10 min 20 sec = [ ( 10 ) ( 60 ) + 20 ] s = 620 s = 620 3600 hr The total time is written as follows: 620 3600 = t 1 + t 2 + t 3 + t 4 + t 5

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Vector Mechanics for Engineers: Dynamics

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The magnitude of acceleration.

Solution Summary: The car starts from rest and accelerates at constant speed, then decelerates at the same rate until it completes 8miles from the start.

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