Deriving Motion Equations

The video tutorial explains the derivation of the equation for displacement, s = ut + 1/2 at^2. It begins by introducing the concept of average velocity as the mean of initial and final velocities. The tutorial then substitutes the velocity equation v = u + at into the average velocity formula. It further relates velocity to displacement over time, leading to the final derivation of the displacement equation. The process involves algebraic manipulation and substitution to arrive at the desired formula.

What is the equation we are asked to derive in this tutorial?

• s = ut + 1/2 at^2

• v = u + at

• s = vt + 1/2 at^2

• v = s/t

How is average velocity defined in the context of this problem?

• As the sum of initial and final velocities divided by two

• As the product of initial and final velocities

• As the difference between initial and final velocities

• As the initial velocity only

What is the formula for final velocity used in the substitution?

• v = u + at

• v = s/t

• v = ut + 1/2 at^2

• v = u - at

What does the equation v = s/t represent?

• Velocity as displacement over time

• Final velocity

• Initial velocity

• Average velocity

What is the first step in isolating displacement (s) in the equation?

• Add initial velocity (u)

• Subtract acceleration (a)

• Divide by time (t)

• Multiply across by time (t)

What is the result of multiplying t by (2u + at)?

• ut + 1/2 at^2

• s/t

• 2u + at

• 2ut + at^2

How is the term at^2 simplified in the final equation?

• Subtracted from ut

• Multiplied by 2

• Divided by 2

• Added to ut

What is the final form of the equation derived in this tutorial?

• s = u + at

• s = vt + 1/2 at^2

• s = ut + 1/2 at^2

• s = 2ut + at^2

What is the significance of the term 1/2 in the equation s = ut + 1/2 at^2?

• It is the average velocity

• It represents the initial velocity

• It is a correction factor for displacement

• It accounts for the constant acceleration over time

Which of the following is NOT a component of the equation s = ut + 1/2 at^2?

• Final velocity

• Time

• Initial velocity

• Acceleration