You're driving down the highway at 20m/s when you see a dog you don't want to crush it 35 m in front of you. Your reaction time before stepping on the brakes is 0.5s, and acceleration created by your brakes is 10 m/s^2 what was the distance travelled before coming to a stop?
did that just below.
S = ut + at*2/2
s= 20 * 0.5 + 10(0.5)*2
s= 10 + (10 * .25) /2
S = 10 + 1.25
S = 11.25 Meters
To calculate the distance traveled before coming to a stop, we need to consider the initial velocity, reaction time, braking acceleration, and the distance to the dog.
Given:
- Initial velocity (u) = 20 m/s
- Reaction time (t1) = 0.5 s
- Braking acceleration (a) = -10 m/s^2 (negative because it is a deceleration)
- Distance to the dog (s) = 35 m
First, we calculate the distance covered during the reaction time using the equation:
Distance during reaction time (d1) = u * t1
d1 = 20 m/s * 0.5 s
d1 = 10 m
Next, we calculate the distance covered while braking using the equation:
Distance during braking (d2) = (u * t2) + (0.5 * a * t2^2)
Here, t2 is the time it takes to stop after the reaction time. To find t2, we use the equation:
Final velocity (v) = u + a * t2
Since the final velocity is 0 m/s (as the car comes to a stop), we can rearrange the equation to solve for t2:
0 m/s = 20 m/s + (-10 m/s^2) * t2
-20 m/s = -10 m/s^2 * t2
t2 = 2 s
Plugging in the values, we can now calculate d2:
d2 = (20 m/s * 2 s) + (0.5 * (-10 m/s^2) * (2 s)^2)
d2 = 40 m + (-20 m)
Finally, we sum up d1 and d2 to find the total distance traveled before coming to a stop:
Total distance = d1 + d2
Total distance = 10 m + 40 m
Total distance = 50 m
Therefore, the total distance traveled before coming to a stop to avoid crushing the dog is 50 meters.