Help me to figure out how this equation is derived

[physiker99]

Hello, I just couldn't understand how solver comes up with the equation at line 5 of the part b. (equates t (time) to other variables). I think the first 4 lines are enough to figure out this equation so i am not posting the question. i will be grateful if you'd help me.http://www.cramster.com/Answer-Board/Image/200863929416334808218196100003057.jpg

 

[Avodyne]

He uses $$R\omega=at$$ (line 3) in line 2, and solves for t.

 

[thomate1]

Hello,

Thank you for reaching out for assistance. In order to understand how the equation is derived, it is important to understand the context and purpose of the equation. From the provided image, it appears that the equation is being used to calculate the distance traveled by an object given its initial velocity and acceleration over a certain period of time.

The equation shown in line 5, d = v0t + 1/2at^2, is known as the displacement formula and is derived from the basic equations of motion in kinematics. It is a combination of the equations for velocity (v = v0 + at) and acceleration (a = (v-v0)/t), where v0 is the initial velocity, a is the acceleration, and t is the time.

The first four lines of the problem provide the necessary information to solve for the displacement using this formula. The initial velocity (v0) is given as 20 meters per second and the acceleration (a) is given as -5 meters per second squared (note the negative sign indicates that the object is decelerating). The time (t) is also given as 4 seconds.

By substituting these values into the displacement formula, we get d = (20)(4) + 1/2(-5)(4)^2 = 80 - 40 = 40 meters. This means that the object traveled a distance of 40 meters over the 4 second time period.

I hope this explanation helps you understand how the equation was derived. If you have any further questions or need clarification, please don't hesitate to ask. Good luck with your studies!