David is driving a steady 30 m/s when he passes tina, who issitting in her car a

Question

David is driving a steady 30 m/s when he passes tina, who issitting in her car at rest. tina begins to accelerate at a steady2.0 m/s^2 at the instant when david passes. a) how far does tina drive before passing david? b) what is her speed as she passes him? David is driving a steady 30 m/s when he passes tina, who issitting in her car at rest. tina begins to accelerate at a steady2.0 m/s^2 at the instant when david passes. a) how far does tina drive before passing david? b) what is her speed as she passes him?

Explanation / Answer

Steady speed (vD) of David = 30 m/s Acceleration (aD) of David = 0, because he is movingwith constant speed. Initial speed (uT) of tina = 0 Acceleration (aT) of tina = 2.0m/s2 Now when she passes him the distance covered by both are equal. So the distance covered by David is xD = vDt+ (1/2)aDt2                                                                                 = (30m/s)t And distance covered by tina is xT = uTt +(1/2)aTt2                                                                      = 0 + (1/2)(2.0m/s2)t2Therefore (30m/s)t= (1/2)(2.0m/s2)t2                        t = 30s Now distance traveled is x = (30m/s)t                                         = (30m/s)(30s) = 900m Tina's speed when she crosses him is                 v = 2ax                    = [2(2.0m/s2)(900m)]                    = 60m/s

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