- #1
Rijad Hadzic
- 321
- 20
Homework Statement
While strolling downtown on a Saturday afternoon you stumble across an old car show. As you are walking along an alley toward a main street, you glimpse a particularly stylish Alpha Romero pass by. Tall buildings on either side of the alley obscure your view, so you see the car only as it passes between the buildings. Thinking back to your physics class, you realize that you can calculate the cars acceleration. You estimate the width of the alley way between the two buildings to be 4 m. The car was in view for .5s. You also heard the engine rev when the car started from a red light, so you know the alpha romero started from rest 2s before you first saw it. Find the magnitude of its acceleration
Homework Equations
[itex] V_{ox} + a_xt = V_x [/itex]
[itex] \Delta x = V_xt - (1/2) a_xt^2 [/itex]
The Attempt at a Solution
So since the car starts from 0 velocity, its final velocity =
[itex] V_x = a_x(t_2) [/itex]
where [itex] t_2 = 2 s[/itex]
its initial velocity [itex] V_{ox} = 2\Delta x + a_xt_1^2 / (2t_1) [/itex] where [itex] t_1 = .5s [/itex]
is = to the final velocity first equation, so the two are =
[itex] 2\Delta x + a_xt_1^2 / (2t_1) = a_x(t_2) [/itex]
now solving
[itex] a_x (2t_1)(t_2) = 2\Delta x + a_x t_1^2 [/itex]
[itex] a_x(2t_1)(t_2) - a_xt_1^2 = 2\Delta x [/itex]
[itex] a_x [ (2t_1)(t_2) - (t_1)^2 ] = 2\Delta x [/itex]
[itex] a_x = (2\Delta x ) / (2t_1)(t_2)-(t_1^2) [/itex]
[itex] = a_x = 8 m / (1s)(2s) - (.5s)^2 = 8m / (1.75 s)^2 = 4.6 m/s^2 [/itex]but my book is telling me my answer is aboout 4 seconds.
My answer is closer to 5 seconds.
Does anyone know what I did wrong? Maybe the way I set up my eq's?