(a) Explanation Given information: At time ( t ) is zero the velocity ( v ) is zero. At time ( t ) is 0.4 sec the position ( x ) is 0.8 ft . Calculation: Show the a-t curve of an accelerometer record for the motion with areas as in Figure (1): Calculate the area ( A 1 ) using the relation: A 1 = 2 3 a ( 16 − 24 ) t 1 Here, a ( 16 − 24 ) is acceleration between 24 ft/s 2 to 16 ft/s 2 and t 1 is time between 0 to 0.2 sec. Substitute 8 ft/s 2 for a ( 16 − 24 ) and 0.2 sec for t 1 . A 1 = 2 3 × 8 × 0.2 = 1.0667 ft/s Calculate the area ( A 2 ) using the relation: A 2 = a ( 0 − 16 ) t 1 Here, a ( 0 − 16 ) is acceleration between 0 ft/s 2 to 16 ft/s 2 . Substitute 16 ft/s 2 for a ( 0 − 16 ) and 0.2 sec for t 1 . A 2 = 16 × 0.2 = 3.2 ft/s Calculate the area ( A 3 ) using the relation: A 3 = ( a ( 0 − 16 ) + a ( 0 − 8 ) 2 ) t 2 Here, a ( 0 − 8 ) is acceleration between 0 ft/s 2 to 8 ft/s 2 and t 2 is time between 0.2 sec to 0.3 sec. Substitute 16 ft/s 2 for a ( 0 − 16 ) , 8 ft/s 2 for a ( 0 − 8 ) and 0 (b) To determine The position of the part at time 0.3 sec ( x 0.3 ) and time 0.2 sec ( x 0.2 ) .

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Chapter 11.3, Problem 11.77P

(a)

To determine

Construct the v-t curve for 0≤t≤0.4sec.

(b)

To determine

The position of the part at time 0.3 sec (x0.3) and time 0.2 sec (x0.2).

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Chapter 11.3, Problem 11.76P

Chapter 11.3, Problem 11.78P

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Construct the v-t curve for 0 ≤ t ≤ 0.4 sec .

Solution Summary: The author shows the a-t curve of an accelerometer record for the motion with areas as in Figure 1.