A car traveling 85km/h slows down at a constant 0.52m/s2 just by "letting up on the gas." Calculate the distance the car coasts before it stops.
vf^2=vi^2+2ad
calculte distance d. change velocity to m/s
23.36^2/2x0.52
=524.70m/s/s
23.36^2/1.04
=524.70m/s/s
To calculate the distance the car coasts before it stops, we can use the equation of motion:
vf^2 = vi^2 + 2ad
where:
vf = final velocity (0 m/s, since the car stops)
vi = initial velocity (85 km/h, which needs to be converted to m/s)
a = acceleration (-0.52 m/s^2, since the car is decelerating)
d = distance
First, we need to convert the initial velocity from km/h to m/s:
85 km/h * (1000 m/1 km) * (1 h/3600 s) = 23.61 m/s (rounded to two decimal places)
Now, we can substitute the values into the equation:
(0 m/s)^2 = (23.61 m/s)^2 + 2 * (-0.52 m/s^2) * d
Simplifying the equation:
0 = (558.5 m^2/s^2) - (1.04 m/s^2) * d
Rearranging the equation to solve for distance, d:
1.04 m/s^2 * d = 558.5 m^2/s^2
d = (558.5 m^2/s^2) / 1.04 m/s^2
d ≈ 537.02 m (rounded to two decimal places)
Therefore, the car will coast for approximately 537.02 meters before it stops.