gogogadget
New member
- Joined
- Jan 29, 2012
- Messages
- 8
I had a question pertaining to physics but I am not sure I understand the steps my problem took it in setting the problem up as a quadratic equaton to solve it. I'll show the steps up to what I understand and how they solved it but they didn't show the specific algebraic steps to how they set up the quadratic equation itself. Many thanks for all who read this.
Problem:
A car traveling at a constant speed of 45.0 m/s (meters per second) passes a trooper on a motorcycle hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets out from the billboard to catch the car, accelerating at a constant rate of 3.00 m/s2. How long does it take the trooper to overtake the car?
So for my equations I have:
vxcar=45.0 m/s
tcar=1 second
axtrooper=3.00 m/s2
Because the car is traveling at a constant velocity, the equation for the constant velocity would be applied to find its final position at 1 second:
x=postion, t=time, v=velocity, a=acceleration
xcar=xi + vxcar
Because the car is moving at a speed of 45.0 m/s, it can be presumed that xicar (initial position) is 45 m when it reaches the sign if t=0 upon passing the sign. Therefore, xcar=45 m.
In looking at the trooper, the trooper starts from rest at ttrooper=0 s. It accelerates at axtrooper=3.00 m/s2. As such, it's position in moving at a constant acceleration can be calculated as shown below:
xf=x + vxi + 1/2axt2 = (0) (0) = 1/2axt2
Therefore: xtrooper=xcar
1/2axt2 = xi + vxcart
1/2axt2 - vxcart - x = 0
From here is where I get confused as the next step they show as:
t = vxcar +/-
v2xcar + 2ax(x)/ax
So I know that they factor out t and get everything else over to one side. I know they take the square root of t to get it on the other side. I don't understand though why there are two "ax's" though. There's the one that is multiplied by 2 and x and then the other that is divided. If someone could show me the step by step process in getting the square root equation for t set up, I'd really appreciate it as my book did not do it and I'm confused. Thank you again!![Big grin :D :D](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Problem:
A car traveling at a constant speed of 45.0 m/s (meters per second) passes a trooper on a motorcycle hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets out from the billboard to catch the car, accelerating at a constant rate of 3.00 m/s2. How long does it take the trooper to overtake the car?
So for my equations I have:
vxcar=45.0 m/s
tcar=1 second
axtrooper=3.00 m/s2
Because the car is traveling at a constant velocity, the equation for the constant velocity would be applied to find its final position at 1 second:
x=postion, t=time, v=velocity, a=acceleration
xcar=xi + vxcar
Because the car is moving at a speed of 45.0 m/s, it can be presumed that xicar (initial position) is 45 m when it reaches the sign if t=0 upon passing the sign. Therefore, xcar=45 m.
In looking at the trooper, the trooper starts from rest at ttrooper=0 s. It accelerates at axtrooper=3.00 m/s2. As such, it's position in moving at a constant acceleration can be calculated as shown below:
xf=x + vxi + 1/2axt2 = (0) (0) = 1/2axt2
Therefore: xtrooper=xcar
1/2axt2 = xi + vxcart
1/2axt2 - vxcart - x = 0
From here is where I get confused as the next step they show as:
t = vxcar +/-
![square-root.jpg](http://2.bp.blogspot.com/_0agwm6I7YZE/TO_DccbrDBI/AAAAAAAAMEU/0OADo56Xqxw/s1600/square-root.jpg)
So I know that they factor out t and get everything else over to one side. I know they take the square root of t to get it on the other side. I don't understand though why there are two "ax's" though. There's the one that is multiplied by 2 and x and then the other that is divided. If someone could show me the step by step process in getting the square root equation for t set up, I'd really appreciate it as my book did not do it and I'm confused. Thank you again!