Answer:
t = 14.9 s
s = 80.3 m
Explanation:
The total acceleration is related to the tangential acceleration and the centripetal acceleration by Pythagorean's theorem. The centripetal acceleration is equal to the square of the tangential velocity divided by the radius. From there, we use kinematics to solve for time and distance traveled.
Using Pythagorean theorem:
a² = at² + ac²
0.83² = 0.72² + ac²
ac = 0.413 m/s²
The tangential velocity is:
ac = v² / r
0.413 = v² / 280
v = 10.75 m/s
Given that initial velocity u = 0 m/s, final velocity v = 10.75 m/s, and tangential acceleration is a = 0.72 m/s², the distance traveled is:
v² = u² + 2as
10.75² = 0² + 2 (0.72) s
s = 80.3 m
And the time traveled is:
v = u + at
10.75 = 0 + (0.72) t
t = 14.9 s
