When you try to stop your car in an emergency, there is some time before you can react.Your car is going 25 m/s and your reaction time is 0.20 s, then after you hit your brakes it decelerates at 9.5 m/s2. How far will your car travel before it stops?
d = 25 * 0.20 + x = 5 + x
x = (25/2) t = (1/2) a t^2
a t = 25
9.5 t = 25
t = 25/9.5 = 2.63 seconds braking
x = (25/2) (2.63) = 32.9
so
d = 5 + 32. 9 = 37.9 meters
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check
v = a t
v = 9.5 * 2.63 = 25 check
x = 12.5 t = 12.5*2.63 = 32.9 check
32.9 + 25*.2 = 37.9 check
It takes t = 25/9.5 seconds to stop once the brakes are applied.
s = 25*0.2 + 25t - 4.75 t^2 is the total stopping distance
d1 = V*T = 25*0.2 = 5 m. = distance traveled during reaction time.
V^2 = Vo^2+2a*d2 = 0
25^2-19*d2 = 0
d2 = 33 m. = distance traveled during deceleration.
d = d1+d2 = 5+33 = 38 m.
To calculate the distance your car will travel before it stops, we can follow these steps:
1. Calculate the distance traveled during the reaction time.
- The formula to calculate distance is: distance = speed × time.
- Given that the speed of the car is 25 m/s and the reaction time is 0.20 s, we can use the formula: distance = 25 m/s × 0.20 s = 5 meters.
- So, during your reaction time, your car will travel 5 meters.
2. Calculate the distance traveled while decelerating.
- The formula to calculate distance when decelerating is: distance = (speed²) / (2 × acceleration).
- Given that the speed of the car is 25 m/s and the deceleration is 9.5 m/s², we can use the formula: distance = (25 m/s)² / (2 × 9.5 m/s²) = 6.58 meters.
- So, while decelerating, your car will travel 6.58 meters.
3. Add the distances traveled during the reaction time and while decelerating.
- 5 meters + 6.58 meters ≈ 11.58 meters.
- Therefore, your car will travel approximately 11.58 meters before it stops in the emergency situation.