Attempting to stop on a slippery road, a car initially moving at 80 km/h skids at 30° to its initial motion, stopping in 3.9 s. Determine the average acceleration in m/s2 in coordinates with the x-axis in the direction of the original motion and the y- axis toward the side to which the car skids.
initial speed = 80,000 m/3600 s = 22.2 m/s
initial x speed = 22.2 cos 30 = 19.25 m/s
final x speed = 0
ax = -19.25/3.9
initial y speed = 22.2 sin 30 = 11.1 m/s
final y speed = 0
ay = -11.1/3.9
To find the average acceleration, we need to determine the change in velocity and the time interval. From the given information, we know that:
Initial velocity (u) = 80 km/h
Skid angle (θ) = 30°
Stopping time (t) = 3.9 s
First, let's convert the initial velocity from km/h to m/s:
1 km/h = 1000 m / 3600 s = 5/18 m/s
So, the initial velocity (u) = 80 km/h = (80 * 5/18) m/s = 200/9 m/s
To find the change in velocity, we need the final velocity (v) of the car. Since the car stops, the final velocity is 0 m/s.
The change in velocity (Δv) = final velocity (v) - initial velocity (u) = 0 - (200/9) m/s = - (200/9) m/s
Next, we can find the average acceleration (a) using the formula:
a = Δv / t
Substituting the values:
a = -(200/9) m/s / 3.9 s = - (200/9) m/s * (1/3.9) s = - (200/9) * (1/3.9) m/s²
Therefore, the average acceleration in m/s² is approximately -0.568 m/s².