find reaction time, given acceleration, displacement, etc

[Clifford]

A car is driving 75.0 km/h [N] when it notices a stalled car 40.8 m directly ahead of him. The car applies the brakes, coming to a stop just in time to avoid a collision. The brakes provid a constant acceleration of 4.80 m/s^2 . What is the reaction time?

our acceleration is 4.80 m/s^2
out initial velocity is 75.0 km/h or 20.8 m/s
our final velocity is 0 m/s
and our displacement is 48.0 m
We are trying to solve for time

apply this data to an equation of t = v / a = 20.8 / 4.8 = 4.3 s

if you apply this data to the equation of t = (2/v) * d = (2 / 20.8) * 48.0 = 4.62 s

What am I doing wrong?

 

[skeeter]

something is not right about this "problem"

vo = 75 km/hr = 125/6 m/s
a = -4.8 m/s²
vf = 0

using the equation \(\displaystyle \L v_f^2 = v_o^2 + 2a(\Delta x}\) ...

\(\displaystyle \L \Delta x = \frac{v_f^2 - v_o^2}{2a} = 45.2 m\)

the 40.8 m given is not enough room to stop.

recheck your given information.

 

[Clifford]

Sorry I did make a typo in the question the given room to stop is 48.0 m. I typed it correctly with the given information that I displayed.

 

[skeeter]

so ... it takes 45.2 m to stop, and the driver saw the car 48 m in front of him.

this means he traveled 48 - 45.2 = 2.8 m before he reacted at a speed of 75 km/hr.

can you figure out the reaction time now?

 

[Clifford]

He traveled 2.8m before he reacted, and he is traveling at a speed of 75 km/h or 125/6 m/s.

v = d/t
t = d/v = 2.8 / (126/6) = 0.1344 = 0.13 seconds

correct?