Given:
v = 22.0m/s
a = -4.00m/s²
Use the equations:
(1) 0 = v + a t
(2) s = v t + a t²/2
Solve (1) for t.
Substitute to solve (2) for s.
v = 22.0m/s
a = -4.00m/s²
Use the equations:
(1) 0 = v + a t
(2) s = v t + a t²/2
Solve (1) for t.
Substitute to solve (2) for s.
1) Distance traveled during the reaction time:
The formula for distance traveled (d) during a constant velocity is given by:
d = v * t
where v represents the initial velocity and t represents the time elapsed.
In this case, the car is traveling at +22.0 m/s, so the initial velocity (v) is +22.0 m/s. The time elapsed (t) is 0.560 s. Plugging these values into the formula, we can find the distance traveled during the reaction time.
d_reaction = v * t
d_reaction = 22.0 m/s * 0.560 s
d_reaction = 12.32 m
Therefore, the distance traveled during the reaction time is 12.32 meters.
2) Distance traveled while decelerating:
The formula for distance traveled (d) during deceleration is given by:
d = (v^2 - u^2) / (2 * a)
where v represents the final velocity, u represents the initial velocity, and a represents the deceleration.
In this case, the car decelerates at 4.00 m/s². The final velocity (v) is 0 m/s since the car stops. The initial velocity (u) is +22.0 m/s. Plugging these values into the formula, we can find the distance traveled while decelerating.
d_deceleration = (v^2 - u^2) / (2 * a)
d_deceleration = (0^2 - 22.0^2) / (2 * -4.00 m/s²)
d_deceleration = (-484.0 m²/s²) / (-8.00 m/s²)
d_deceleration = 60.5 m
Therefore, the distance traveled while decelerating is 60.5 meters.
Now, to find the total stopping distance, we need to sum up the distance traveled during the reaction time and the distance traveled while decelerating.
Total stopping distance = d_reaction + d_deceleration
Total stopping distance = 12.32 m + 60.5 m
Total stopping distance = 72.82 m
Therefore, the stopping distance of the car, as measured from the point where the driver first notices the red light, is approximately 72.82 meters.