Answer:
a. The car sweeps out 0.799 radians per second.
b. f(t) = 8 cos (0.799t)
Step-by-step explanation:
Given that:
The radius r = 8 feet
a.
The time t it takes to complete one full lap = 7.854 seconds
Recall that:
Angular velocity ω = 2π / t
So if in 7.854 seconds, the car sweeps = 2π radian
∴
per second, the car will sweep ω = 2π/ 7.854
ω = 0.799 rad/sec
Thus, the car sweeps out 0.799 radians per second.
b.
Since, r = 8 feet.
Suppose the car travels an angle θ in time (t),
Then the general equation for the horizontal component is:
f(t) = rcos( ωt)
f(t) = 8 cos (0.799t)