2022-04-11

1. At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.20 m/s2. At the same instant a truck, traveling with a constant speed of 20.0 m/s, overtakes and passes the car. (a) How far beyond its starting point does the car overtake the truck? (b) How fast is the car traveling when it overtakes the truck?

nick1337

Expert2022-08-10Added 699 answers

a) Suppose $x\dot{y}$ displacement after which can $\dot{y}$ overtaking the truck

car: $x=\frac{1}{2}\times 3.20\times {t}^{2}=1.6{t}^{2}$

truck: $x=20t$

$1.6{t}^{2}=20t\to t=\frac{20}{1.6}=12.52$

$\to x=20\times 12.5=250m$

Car overtakes the truck after a distance of 250 m from starting point

b) ${v}_{c}=at=3.20\times 12.5=40\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

speed of car = $40\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

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