Explanation Given information: The motion of an object along the straight line is provided by s ( t ) = 1 2 a t 2 + v 0 t + s 0 , where, s ( t ) is the position relative to the origin at time t . The observed data is ( 1 , 30 ) , ( 2 , 54 ) and ( 3 , 82 ) Formula used: Step 1: Write each equation in the standard form of A x + B y + C z = D . Step 2: Choose the pair of equation and eliminate any one variable by the addition method. Step 3: Choose the different pair of variable and eliminate the same variable. Step 4: The resulting system has two variables. Solve this system by using substitution or addition method. Step 5: Substitute the value of variables found in step 4 into any of the three original equations that contains the third variable. Solve for the third variable. Step 6: Check the order triple in each original equation. Then write the solution as an order triple in set notation. Calculation: Consider the expression as, s ( t ) = 1 2 a t 2 + v 0 t + s 0 The observed data points are ( 1 , 30 ) , ( 2 , 54 ) and ( 3 , 82 ) Therefore, consider the point as, ( 1 , 30 ) , ( 2 , 54 ) , and ( 3 , 82 ) Substitute s ( 1 ) = 30 and t = 1 in the expression s ( t ) = 1 2 a t 2 + v 0 t + s 0 as, 1 2 a + v 0 + s 0 = 30 …… (1) Substitute s ( 2 ) = 54 and t = 2 in the expression s ( t ) = 1 2 a t 2 + v 0 t + s 0 as, 2 a + 2 v 0 + s 0 = 54 …… (2) Substitute s ( 3 ) = 82 and t = 3 in the expression s ( t ) = 1 2 a t 2 + v 0 t + s 0 as, 9 2 a + 3 v 0 + s 0 = 82 …… (3) Multiply equation (1) by − 2 as: − a − 2 v 0 − 2 s 0 = − 60 …… (4) Eliminate v 0 from equation (4) and (2) as: − a − 2 v 0 − 2 s 0 = − 60 2 a + 2 v 0 + s 0 = 54 _ a s 0 = − 6 Thus, the evaluated equation is: a − s 0 = − 6 …… (5) Multiply equation (1) by − 3 : − 3 2 a − 3 v 0 − 3 s 0 = − 90 …… (6) Eliminate v 0 from equation (5) and (3) as, − 3 2 a − 3 v 0 − 3 s 0 = − 90 9 2 a + 3 v 0 + s 0 = 82 _

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Author: Miller

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Chapter 5.2, Problem 53PE

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To calculate: The value of a, v0, and s0, where the motion is an object along the straight line is provided by s(t)=12at2+v0t+s0.

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Chapter 5.2, Problem 52PE

Chapter 5.2, Problem 54PE

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The value of a , v 0 , and s 0 , where the motion is an object along the straight line is provided by s ( t ) = 1 2 a t 2 + v 0 t + s 0 .

Solution Summary: The author explains how to calculate the value of a,v_0 and s(t)=12at

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To calculate: The value of a, v0, and s0, where the motion is an object along the straight line is provided by s(t)=12at2+v0t+s0.

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Chapter 5 Solutions