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A child operating a radio-controlled model car on a dock accidentally steers it off the edge. The car's displacement 1.0 s after leaving the dock has a magnitude of $8.5 m$ . What is the car's speed at the instant it drives off the edge of the dock?
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Answer

$v_{0} = 13.4 m / s$

Steps

Step 1 ：Given the displacement $d = 8.5 m$ , time $t = 1.0 s$ , and acceleration due to gravity $a = - 9.8 m / s^{2}$ .

Step 2 ：Use the kinematic equation: $d = v_{0} t + 0.5 a t^{2}$ to solve for the initial speed $v_{0}$ .

Step 3 ：Rearrange the equation to solve for $v_{0}$ : $v_{0} = \frac{d - 0.5 a t^{2}}{t}$ .

Step 4 ：Substitute the given values: $v_{0} = \frac{8.5 - 0.5 (- 9.8) ({1.0}^{2})}{1.0}$ .

Step 5 ：Calculate the initial speed: $v_{0} = 13.4 m / s$ .

Step 6 ： $v_{0} = 13.4 m / s$