A small object moves along the x axis with acceleration axt...

A small object moves along the x-axis with acceleration ax(t) = -(0.0320 m/s^3)(15.0 s - t). At t = 0, the object is at x = -14.0 m and has velocity v0x = 9.10 m/s. (a) What is the x-coordinate of the object when t = 10.0 s? Express your answer with the appropriate units.

Transcript

00:01 Hey everyone, welcome back.

00:01 In this question we are given that an object moves along x -axis and its acceleration as a function of time is given as minus 0 .320 into 15 minus t.

00:16 This is acceleration of the particle moving along the x -axis.

00:20 Now we are given that at time t is equals to 0 second its position is minus 14 meter and at the same time its velocity is 9 .10 meter per second.

00:33 Now we have to find out its position at t is equals to 10 second at t is equals to 10 second we have to find out its position.

00:43 So as we know that acceleration is nothing but rate of change of velocity with respect to time so this can be written as if i differentiate this function then this will be basically this is divy over d t this is same which is minus 0 .0 .0.

01:00 3 to 0 multiplied with 15 minus t this is the acceleration which is already given now since i have to find out position so i need velocity first then after that from velocity i will find out the position so first the velocity which is dv this will be given by minus 0 .03 to 0 multiplied with 15 minus t into d t and if i integrate both sides then the velocity will be given by this will be integration of this thing and that is 0 320 into t squared divided by 2 minus 0 .48 into t plus c okay now since we are given that at t is equals to 0 velocity is 9 .10 so if i put t is equals to 0 only c will remain and c is 9 .10 because on right -hand side i will have to put 9 .10 so velocity function arrives as 0 .0, 320 t squared divided by 2 minus 0 .48 into t plus c which is 9 .10.

02:06 Okay.

02:07 Now as we know that velocity can be written as rate of change of displacement with respect to time.

02:12 Okay.

02:13 So from here i can write this dx.

02:17 I can write this dx as this function into dt.

02:22 This function into dt...