A car leaves an intersection after a light turns green. It starts from rest and reaches a speed of 13.4 m/s in 5.0 s. The radius of a tire of the car is 0.25 m.
and the question is?
What is the question?
a = (13.4-0)/5 m/s^2 = r*alpha
v = 0 + a t = r*omega
d = 0 + 0t + (1/2)(5)t^2
what is the rotational acceleration?
To solve this problem, we need to use the equations of motion. The equation we'll be using is:
v = u + at
Where:
v = final velocity (13.4 m/s)
u = initial velocity (0 m/s, since the car starts from rest)
a = acceleration (we need to find this)
t = time (5.0 s)
First, we'll rearrange the equation to solve for acceleration:
a = (v - u) / t
a = (13.4 m/s - 0 m/s) / 5.0 s
a = 13.4 m/s / 5.0 s
a = 2.68 m/s²
Now that we know the acceleration, we can find the centripetal acceleration (ac) using the formula:
ac = v² / r
Where:
v = velocity (13.4 m/s)
r = radius of the tire (0.25 m)
ac = (13.4 m/s)² / 0.25 m
ac = 179.96 m²/s² / 0.25 m
ac = 719.84 m/s²
Therefore, the centripetal acceleration of the car is 719.84 m/s².