The angular position of a rotating object is given by the...

The angular position of a rotating object is given by the equation θ = a + bt + ct^2 where a, b, and c are constants. Here a = 1.48 rad, b = 1.94 rad/s, and c = 3.06 rad/s^2. (a) What is the position of the object at t1 = 0 and t2 = 3.80 s? θ1 = 1.48 rad θ2 = 26.032 rad (b) What is the angular speed of the object at t1 = 0 and t2 = 3.80 s? ω1 = 1.94 rad/s ω2 = 11.652 rad/s (c) What is the angular acceleration of the object at t1 = 0 and t2 = 3.80 s? α1 = 3.06 rad/s^2 α2 = 3.06 rad/s^2

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0:00 Hello everyone.

00:01 In this particular question we are given with angular position of our object and angular position is given as a function of time as a plus b t plus c t square.

00:11 Now here the value of a is given as 1 .48 radiance the value of b is given as 1 .94 radian per second and at last the value of c is given in the question as 3 .06 radian per second square.

00:30 Now in the question, in the first part of question we are asked to find out the angular position at 2 times at t1 is equal to 0 second and second at t2 is equals to 3 .80 second.

00:44 Now as we know this is given as angular position so if i put 0 in this particular equation then theta not which is the angular position at t1 equals to 0 this is coming out as a and the value of a is 1 .48 radian.

00:59 Now similarly if i put t2 as 3 .80 second in this particular equation then this will come out as this will come out as a which is 1 .48 plus bt that means 1 .94 into t which is 3 .80 plus c t square that means 3 .06 into 3 .80 whole square.

01:22 Now if we calculate this value then so this particular value is equals to 53 .0 4 .5.

01:30 4 to radiance.

01:32 Now in the second part of question we are asked to find out angular velocity at two different time at t1 is equal to 0 and t2 is equals to 3 .80 second t2 is equal to 3 .80 second now as we know that angular velocity is nothing but rate of change of angular displacement with respect to time so basically if i differentiate the given equation a plus b t plus c t square then this is coming out as b plus 2 c t b plus 2 c t...

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