Constant Acceleration Automobile

[AnkhUNC]

[SOLVED] Constant Acceleration

Homework Statement

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.1 m/s^2. At the same instant a truck is 10.2 m down the road and traveling with a constant speed of 8.5 m/s. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be traveling at that instant?

Homework Equations

The Attempt at a Solution

s(t) = 1/2 a * t^2 + v0 * t + s0
a = acceleration
v0 = initial speed
s0 = initial position


Being for the truck
a = 0 m/s^2
v0 = 8.5 m/s
s0 = 10.2 m
and being for the car
a = 2.1 m/s^2
v0 = 0 m/s
s0 = 0 m
the equation will be:
8.5 m/s * t + 10.2 m = (There is a 1/2 here right?) (1/2)2.1 m/s^2 * t^2

Solving this I get 9.156s which is apparently incorrect.

 

[G01]

I believe the equation you set up is correct. Can you show your math?

 

[AnkhUNC]

Well the math is kinda already there QQ I just plugged it into quadratic equation.

 

[AnkhUNC]

OK I got it!

s(9.16) = 1/2 (2.1) * (9.16)^2 = 88.1 meters

and after 9.16 seconds, it is traveling
v = at
v = 2.1(9.16) = 19.2 m/s

 

[G01]

Awesome! Good job!