Abar on a hinge starts from rest and rotates with an angular acceleration α = 13 + 7t, where α is in rad/s2 and t is in seconds. determine the angle in radians through which the bar turns in the first 4.69 s.

Explanation:

Angular acceleration of the bar, ..........(1)

We need to find the angle in radians through which the bar turns in the first 4.69 s.

We know that,

is angular velocity

On integrating equation (1) wrt t

...............(2)

Also,

On integrating equation (2) wrt t as :

At t = 4.69 s

Hence, this is the required solution.

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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