A car is driving at a speed of 66.0 km/h toward an intersection just as the light changes from green to yellow. The driver has a reaction time of 0.750 s and the magnitude of the braking acceleration of the car is 5.50 m/s2.Find the minimum distance
the car travels before coming to a stop after the light changes.
To find the minimum distance the car travels before coming to a stop after the light changes, we need to consider two parts: the distance traveled during the driver's reaction time and the distance traveled while braking.
1. Distance during the driver's reaction time: Multiply the car's speed by the driver's reaction time to find the distance traveled during this time. Convert the car's speed from km/h to m/s by dividing it by 3.6.
Distance = Speed * Time
Distance = (66.0 km/h / 3.6) * 0.750 s
2. Distance while braking: We will use the equation of motion to calculate the distance traveled during braking.
v^2 = u^2 + 2as
Here:
v = final velocity of 0 m/s, since the car comes to a stop
u = initial velocity, which is the car's speed in m/s after converting it from km/h
s = distance to be determined
a = magnitude of the braking acceleration
Rearrange the equation to solve for s:
s = (v^2 - u^2) / (2a)
s = (0 m/s - (66.0 km/h / 3.6)^2) / (2 * 5.50 m/s^2)
3. Total distance traveled:
Total distance = Distance during reaction time + Distance while braking
Add the distances calculated in steps 1 and 2 to get the total distance the car travels before coming to a stop after the light changes.
Plug the given values into the equations and calculations above to find the minimum distance the car travels before stopping.
V = 68km/h = 68000m/3600s = 18.9 m/s.
d = v*t + 0.5a*t^2.
d = 18.9*0.75 - 0.5*5.5*0.75^2 = 12.6 m.