An automobile and a truck start from rest at the same instant, with the automobi

Question

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2.06m/s2 , and the automobile an acceleration of 3.39m/s2 . The automobile overtakes the truck after the truck has moved a distance 40.0m .

How much time does it take the automobile to overtake the truck?

How far was the automobile behind the truck initially?

What is the speed of the truck when they are abreast?

What is the speed of the automobile when they are abreast?

Explanation / Answer

xtruck = 0.5*2.06*t^2
x car = -d + 0.5*3.39*t^2

we are told that xtruck = 40

40 = 0.5*2.06*t^2
t=6.23 s

40 = -d + 0.5*3.39*6.23^2
d=25.79 m

v truck = 2.06*6.23=12.83 m/s

vcar = 3.39*6.23=21.12 m/s

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