1. Given that the position of a particle is defined in terms...

1. Given that the position of a particle is defined in terms of time by the equation below, where x is in meters and t is in seconds, determine: x = (4t^6 + t^0) / t + (3t^0 / t^6) + 4 (a) the average velocity of the particle from t = 1.0 s to t = 3.0 s, (Ans: v_avg = 16 m/s) (b) the instantaneous velocity of the particle at t = 2.5 s, (Ans: v_t = 20.52 m/s) (c) the average acceleration of the particle from t = 2.0 s to t = 3.0 s, and (Ans: a_avg = 8.42 m/s^2) (d) the t at which the instantaneous acceleration of the particle is 8.10 m/s^2. (Ans: t = 3.91 s)

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00:01 Hello, the question is taken from physics and the question is given that the position of particle is defined in terms of time by the equation below where x is in meter t is in second determined given that x is equal to 4 t.

00:14 I'm just dividing it by t plus 1 by t plus 3 by t to the power 6 plus 4.

00:22 Okay and we know that what is the average velocity from t is equal to 1 to t is equal to 3.

00:31 Okay, so we know that a v average is equal to x2 minus x1 total distance traveled by total time taken.

00:40 Okay, total distances basically 4 into 3 to the power 5.

00:44 So that will be 4 into 3 to the power 5.

00:49 So that is 9 .7 2 plus 1 by 3 plus 1 by 3 to the power 5 plus 4 minus 4 minus 1 minus 1.

01:01 3 minus 4 divided by 3 minus 2 that is 3 minus 1 that is 2 so 4 will be cancelled out and this value will this will give you the value we average is equal to 9 7 2 plus 1 by 3 plus 1 by 3 to 2 to the power 5 and minus 8 divided by 2 so that is 4 8 8 2 .2 meter per second which is the required value of the average velocity okay i think something wrong with the statement that will be 40 square okay if we take it 40 square then it will be 9 into 4 36 so 36 6 minus 8 divided by 2 so that is close to 15 okay so i think it will be t square, no t.

02:11 So, so it t cube, no t to the power six.

02:14 You can check the exact value, but i'm solving it by taking it as t to the power six.

02:20 Instantaneous velocity is just dx over dt.

02:25 Okay.

02:26 At a particular time instant, that is 2 .5...

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