A car is heading towards a brick wall at 80 km/hr, he starts breaking 30 feet away. What acceleration is required to avoid a collision?
The car needs to decelerate at a rate "a" such that sqrt(2aX) = V
a = V^2/(2 X)
To get the answer in m/s^2, you first need to convert the speed V to m/s and the distance X to meters.
He needs to brake to avoid breaking. Note the spelling of those different words.
Vo=80,000m/h * (1/3600)h/s = 22.22m/s.
d = 30ft * (1/3.3)m/ft = 9.09m.
Vf^2 = Vo^2 + 2ad,
a = (Vf^2-Vo^2) / 2d,
a = (0-493.73) / 18.18 = - 27.2m/s^2.
To calculate the acceleration required to avoid a collision, we need to use a physics equation. The equation that relates acceleration (a), initial velocity (u), final velocity (v), and distance (d) is:
v^2 = u^2 + 2ad
In this case, the car is heading towards a brick wall, so the final velocity we want is 0 km/hr (to avoid a collision). The initial velocity (u) is 80 km/hr, which we need to convert to m/s for consistent units. The conversion factor from km/hr to m/s is 1 km/hr = 0.2778 m/s. So u = 80 km/hr * 0.2778 m/s per km/hr.
Now, let's calculate the distance (d) from the wall. Given that the car starts braking 30 feet (which is around 9.14 meters) away from the wall, we can set d = 9.14 m.
Plugging these values into the equation, we have:
(0 m/s)^2 = (80 km/hr * 0.2778 m/s per km/hr)^2 + 2a * 9.14 m
Simplifying the equation, we get:
0 = (22.22 m/s)^2 + 18.28 a
Now, solve for the acceleration (a):
18.28 a = - (22.22 m/s)^2
a = - (22.22 m/s)^2 / 18.28 m
a ≈ -27 m/s^2
Therefore, the acceleration required to avoid a collision is approximately -27 m/s^2. The negative sign indicates that the car needs to decelerate or brake.
Note: Keep in mind that this calculation assumes a constant acceleration throughout the deceleration process, which may not be entirely accurate in real-life situations where braking systems and tire traction come into play.