The distance traveled is 140 radians.
The distance traveled by the object can be determined by first determining the angular acceleration followed by using the third kinematics equation of motion.
From the parameters given:
- the initial angular velociy = 3 rad/s
- the final angular velocity = 25 rad/s
- the time of motion = 10 s
The angular acceleration of an object in motion is the change in the angular velocity with time.
∴
[tex]\mathbf{\alpha = \dfrac{\omega_f - \omega_i}{t}}[/tex]
[tex]\mathbf{\alpha = \dfrac{(25- 3)rad /s}{10\ s}}[/tex]
[tex]\mathbf{\alpha = \dfrac{(22)}{10} \ rad/s^2}[/tex]
[tex]\mathbf{\alpha = 2.2 \ rad/s^2}[/tex]
By using the third kinematics equation of motion:
[tex]\mathbf{\Delta x = \omega_it+ \dfrac{1}{2 }\alpha t^2}[/tex]
- where the distance traveled = Δx
[tex]\mathbf{\Delta x = 3 \ rad/s \times (10) \ s + \dfrac{1}{2 }(2.2\ rad/s^2)(10 \ s) ^2}[/tex]
[tex]\mathbf{\Delta x = 30 \ rad + 110 \ rad}[/tex]
[tex]\mathbf{\Delta x = 140 \ rad}[/tex]
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