If its angular acceleration is constant and equal to 0.200 rad/s2, what is its angular velocity at t = 2.50 s? (assume the acceleration and velocity have the same direction)

Hi!

The angular acceleration is given by:
a = Δω/t

Where ω is the angular velocity and t is the time.

We have 0.2 rad/s² for the acceleration and 2.5s for the time. Since velocity and acceleration have the same direction, we must have ω > ω₀ (final velocity is higher than the initial one), and then a will be a positive number.

a = (ω - ω₀)/t
at = ω - ω₀
ω = at + ω₀
ω = 0.2 x 2.5 + ω₀
ω = 0.5 + ω₀

;)

Answer: it will take   4.36 seconds to reach her average velocity 10.69 miles/hour.explanation:   we have equation of motion ,where s is the displacement, a is the acceleration, u is the initial velocity and t is the time taken.average velocity = displacement/ time taken.average velocity = 10.69 miles/hr = 10.69*1.6*1000/(60*60) = 4.75 m/s4.75 = s/ts = 4. 1we also have acceleration = 2.18 m/s², initial velocity = 0 m/sso it will take   4.36 seconds to reach her average velocity 10.69 miles/hour.