The velocity vector of the insect make an angle of 36.0° clockwise from the x-axis at t = 2.91 s
<h3>Further explanation</h3>
Acceleration is rate of change of velocity.


<em>a = acceleration ( m/s² )</em>
<em>v = final velocity ( m/s )</em>
<em>u = initial velocity ( m/s )</em>
<em>t = time taken ( s )</em>
<em>d = distance ( m )</em>
Let us now tackle the problem!
<u>Given:</u>
![r = [2.90 +(0.0900t^2)]i - [(0.0150)t^3]j](https://tex.z-dn.net/?f=r%20%3D%20%5B2.90%20%2B%280.0900t%5E2%29%5Di%20-%20%5B%280.0150%29t%5E3%5Dj)
To find the velocity function, we will derive the position function above.
![v = dr/dt = [0 +(0.0900)(2t)]i - [(0.0150)(3t^2)]j](https://tex.z-dn.net/?f=v%20%3D%20dr%2Fdt%20%3D%20%5B0%20%2B%280.0900%29%282t%29%5Di%20-%20%5B%280.0150%29%283t%5E2%29%5Dj)
![v = [0.18t]i - [0.045t^2]j](https://tex.z-dn.net/?f=v%20%3D%20%5B0.18t%5Di%20-%20%5B0.045t%5E2%5Dj)
Next to calculate the angle , we use this following formula:





<h2>Conclusion:</h2>
The velocity vector of the insect make an angle of 36.0° clockwise from the x-axis at t = 2.91 s
<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Physics
Chapter: Kinematics
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle