Question

A car and a truck start from rest at the same instant, with the car initially...

A car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of 2.10 m/s2, and the car has a constant acceleration of 3.40 m/s2. The car overtakes the truck after the truck has moved
60.0 m.
a) How much time does it take the car to overtake the truck?
b) How far was the car behind the truck initially?
c) What is the speed of each when they are abreast?
d) On a single graph sketch the position of each vehicle as a function of time. Take x=0 at the initial location of the truck.
Science   Physics   
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Answer #1

ANS a -> ac - acceleration of car, at - acceleration of truck , the initial velocities of both the car and the truck are zero.

Car requires as much time to overtake the truck as needed as the truck has already moved a distance of S = 60.0 m. Equation of motion of the truck :

ST =

t = = = 7.55 s

ANS b-> to find the distance L we need to find the difference in distance that the car and truck drove. Equations of motions for the car

Sc = = = 96.90 m

L = Sc - ST = 96.90 m - 60.0 m = 36.9 m

ANS c -> speed of the truck when they are abreast ,

VT = aT * t = 2.10 * 7.55 = 15.85 m/s

speed of the car when they are abreast,

Vc = ac * t = 3.40 * 7.55 = 25.67 m/s

ANS d -> position time graph of the truck and the car

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