At the instant the traffic light turns green an automobile s

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 1.90 m/s2. At the same instant a truck, traveling with a constant speed of 9.30 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be traveling at that instant?

(a) Number ___Units____

(b) Number______ Units_____

Solution

truck V=9.3 m/s

car a= 1.9 m/s^2 from rest at t=0

Let St, Sc be the distance covered by truck and car respectively for the overtaking to take place.

St=v*t

Sc=0.5*a*t^2

They move the same distance in same time

St=Sc

solve for time

9.3*t=0.5*1.9*t^2

t=9.3/(0.5*1.9) = 9.79 s*****

a) How far beyond the starting point will the car overtake the truck?

Solve either of the equation to get the result.

St=9.3*9.79 = 91.04 m *****

Sc=0.5*1.9*(9.79)^2 = 91.04 m *****

b) How fast will the car be traveling at that instant?

V = at

v=1.9*9.79 = 18.6 m/s *****