△ X = V 0 T + 1 / 2 a T 2 − 45...

Alonzo Odom

Alonzo Odom

Answered

2022-07-26

X = V 0 T + 1 / 2 a T 2
45 m = 10 m / s T 4.90 m / s 2 T 2

Answer & Explanation

umshikepl

umshikepl

Expert

2022-07-27Added 11 answers

Since you have two equations, and both have a T and T 2 term, you can rewrite the second equation to have T 2 interms of T : 4.90 m / s 2 T 2 = 45 m 10 m / s T.
Multiply through by ( 1 ) : 4.90 m / s 2 T 2 = 45 m + 10 m / s T.
Divide through by ( 4.90 m / s 2 ) : T 2 = ( 45 s 2 / 4.90 ) + ( 10 s / 4.90 ) T.
Now, plug this equation into the first equation: X = V 0 T + 1 / 2 a T 2 = V 0 T + 1 / 2 a [ ( 45 s 2 / 4.90 ) + ( 10 s / 4.90 ) T ].
Multiply through: X = V 0 T + 45 s 2 / 9.80 + 10 s T / 9.80.
Multiply all by ( 9.80 ) : 9.80 X = 9.80 V 0 T + 45 s 2 + 10 s T.
Add like terms: 9.80 X = T ( 9.80 V 0 + 10 s ) + 45 s 2 . Your solution, then, gives X in terms of T and V 0 .

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