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5. Car `A` and car `B` are `1000\ m` apart. Both cars start at the same time and drive toward each other. Car `A` travels at a rate of `7.0\ m//s` and car `B` travels `3.0\ m//s`. In how many seconds will the two cars meet?
5. Car A and car B are 1000\ m apart. Both cars start at the same time and drive toward each other. Car A travels at a rate of 7.0\ m//s and car B travels 3.0\ m//s. In how many seconds will the two cars meet? `x_f = x_i + v∆t`
`∆t = 100\ s`
Given:
`d = 1000\ m`
`v_A = 7.0\ m//s`
`v_A = -3.0\ m//s`
`x_(A_i) = 0\ m`
`x_(B_i) = 1000\ m`
Equation:
`x_f = x_i + v∆t`
Solution:
`x_(A_f) = x_(A_i) + v_A ∆t`
`x_(B_f) = x_(B_i) + v_B ∆t`
At the moment 2 cars meet together, `x_(A_f) = x_(B_f)` We get
`x_(A_i) + v_A ∆t = x_(B_i) + v_B ∆t`
`v_A ∆t- v_B ∆t = x_(B_i) - x_(A_i) `
`(v_A - v_B) ∆t = x_(B_i) - x_(A_i) `
`∆t = (x_(B_i) - x_(A_i))/(v_A - v_B) `
`∆t = (1000\ m - 0)/( 7.0\ m//s - (-3.0\ m//s)) `
`∆t = 100\ s` |