Approaching one of the many sharp horizontal turns in the Monaco Grand Prix, an experienced Formula-1 driver slows down from 125 km/h to 53.0 km/h while rounding the bend in 12.0 s. If the driver continues to decelerate at this same rate and the radius of the curve is 15.0 m, what is the acceleration of the car the moment that its speed reaches 53.0 km/h? (Enter the magnitude.)
m/s2
To find the acceleration of the car at the moment its speed reaches 53.0 km/h, we need to convert the speed from km/h to m/s.
Given:
Initial speed (v_0) = 125 km/h = 34.72 m/s
Final speed (v_f) = 53.0 km/h = 14.72 m/s
Time taken (t) = 12.0 s
Radius of the curve (r) = 15.0 m
We can calculate the acceleration using the following kinematic equation:
v_f^2 = v_0^2 + 2ad
Where:
v_f = final speed
v_0 = initial speed
a = acceleration
d = distance
Since the car is slowing down, the acceleration is negative (-a). We can rearrange the equation to solve for acceleration:
a = (v_f^2 - v_0^2)/(2d)
Let's substitute the given values into the equation to find the acceleration:
a = (14.72^2 - 34.72^2)/(2 * 15.0)
a = (216.6784 - 1206.5984)/30.0
a = -990.92/30.0
a = -33.03 m/s^2
Therefore, the acceleration of the car at the moment its speed reaches 53.0 km/h is 33.03 m/s^2 (magnitude).
To find the acceleration of the car when its speed reaches 53.0 km/h, we need to first find the initial speed of the car, final speed of the car, and the time taken to decelerate.
Given:
Initial speed (u) = 125 km/h
Final speed (v) = 53.0 km/h
Time taken (t) = 12.0 s
Radius of the curve (r) = 15.0 m
To find the initial and final speeds in m/s, we need to convert them from km/h to m/s. We can use the following conversion factor:
1 km/h = 0.2778 m/s
Initial speed (u) = 125 km/h * 0.2778 m/s = 34.7 m/s
Final speed (v) = 53.0 km/h * 0.2778 m/s = 14.7 m/s
We can find the acceleration (a) by using the formula:
a = (v - u) / t
Substituting the values:
a = (14.7 m/s - 34.7 m/s) / 12.0 s
Simplifying further:
a = (-20.0 m/s) / 12.0 s
a = -1.67 m/s^2
Therefore, the acceleration of the car when its speed reaches 53.0 km/h is approximately 1.67 m/s^2.
The linear acceleration and the centripetal acceleration are perpendicular to each other so the magnitude is the square root of the sum of the squares.
linear
al = change in velocity/time
=[(53-125)km/h * 1000m/km /3600s/h] /12s
ac = v^2/r = [53/3.6]^2/15
then a = sqrt(al^2+ac^2)