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A wheel has a constant angular acceleration of 1.8 rad/s2. During a certain 4.0 s interval, it turns through an angle of 45 rad. Assuming that the wheel started from rest, how long had it been in motion before the start of the 4.0 s interval?

User Jecoms
by
7.9k points

1 Answer

3 votes

Answer:

4.25 s

Step-by-step explanation:

Given:

angular acceleration'α'= 1.8 rad/s²

angle 'θ'= 45 rad

time 't'= 4s

initial angular velocity '
w_(o)'=0
rad^(-1)

as we know that,

θ=
w_(1)t +
(1)/(2) \alpha t^(2)

45 = 4
w_(1) + (0.5 x 1.8 x 16)

45- 14.4 = 4
w_(1)

30.6 = 4
w_(1)


w_(1)= 7.65
rad^(-1)

Next is to find t by using the equation


w_(1) =
w_(o) +
\alpha t_(1)

7.65= 0 + (1.8)
t_(1)


t_(1)= 7.65/1.8


t_(1)= 4.25 s

Therefore, At the start of 4s interval the motion is at 4.25 second

User Rob Drimmie
by
8.7k points

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