A car moving with a speed of 85 km/h is brought to rest in a didtance of 60 m. How much time did the car take to stop?
Average speed x time = stopping distance
The average speed during stopping is half the starting speed, or 42.5 km/h
85 km/h = 23.6 m/s
42.5 km/h = 11.8 m/s
Time = 60m/11.8m/s = 5.1 seconds
To find the time it took for the car to stop, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, since the car comes to rest)
u = initial velocity (85 km/h or 85 * (1000/3600) m/s)
s = distance traveled (60 m)
a = acceleration
Solving for time (t):
v^2 = u^2 + 2as
Substituting the given values:
0 = (85 * (1000/3600))^2 + 2 * a * 60
To find the acceleration (a), we can rearrange the equation:
a = (0 - (85 * (1000/3600))^2) / (2 * 60)
Now we can substitute the value of acceleration back into the equation to solve for time:
0 = (85 * (1000/3600))^2 + 2 * ((0 - (85 * (1000/3600))^2) / (2 * 60)) * t
Simplifying the equation:
0 = (85 * (1000/3600))^2 - ((85 * (1000/3600))^2) / 30 * t
Now we can solve for t:
0 = ((85 * (1000/3600))^2) * (1 - (1/30) * t)
Divide both sides by ((85 * (1000/3600))^2):
0 = 1 - (1/30) * t
Rearrange the equation:
(1/30) * t = 1
Multiply both sides by 30:
t = 30
Therefore, the car took 30 seconds to stop.