A car is traveling at a constant velocity of 21 m/s (about 45 mph). The driver sees a fallen tree lying across the road and hits the brakes after a delay (reaction time) of 245 ms. (1 ms = 10-3 s.)
Calculate the distance the car travels during this 245 ms reaction time period.
Once the brakes are applied, the car slows to a stop with an acceleration of -5.29 m/s2. Calculate the distance the car travels while the brakes are applied.
d = Vo*t = 21m/s * 0.245s =
V^2 = Vo^2 + 2a*d.
V = 0.
Vo = 21 m/s.
a = -5.29 m/s.
d = ?.
89
To calculate the distance the car travels during the reaction time period, we can use the formula:
Distance = Velocity x Time
Given that the velocity of the car is 21 m/s and the reaction time is 245 ms, we need to convert the reaction time to seconds by dividing it by 1000:
Reaction Time = 245 ms ÷ 1000 = 0.245 s
Now, we can calculate the distance during the reaction time:
Distance = Velocity x Reaction Time
Distance = 21 m/s x 0.245 s
Distance ≈ 5.145 m
Therefore, the car travels approximately 5.145 meters during the reaction time period.
Now, let's calculate the distance the car travels while the brakes are applied. We can use the following kinematic equation:
Distance = (Velocity^2 - Initial Velocity^2) / (2 x Acceleration)
Given that the initial velocity is 21 m/s, and the acceleration is -5.29 m/s^2, we can calculate the distance:
Distance = (0^2 - (21^2)) / (2 x -5.29)
Distance = (-441) / (-10.58)
Distance ≈ 41.722 m
Therefore, the car travels approximately 41.722 meters while the brakes are applied.