Equations of Uniform Accelerated Motion Physics Mrs Coyle

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Equations of Uniform Accelerated Motion Physics Mrs. Coyle

Equations of Uniform Accelerated Motion Physics Mrs. Coyle

Average Velocity � v = ½ (vf +vi)

Average Velocity � v = ½ (vf +vi)

• Displacement in terms of Average Velocity and Time � d= v t

• Displacement in terms of Average Velocity and Time � d= v t d= ½ (vf + vi) t

How do we derive d= ½ (vf + vi)t from the graph? Velocity (m/s)

How do we derive d= ½ (vf + vi)t from the graph? Velocity (m/s) vf vi o t Time (s) • Hint: Area Under the Line=Displacement Δd or simply d

Displacement (d) in terms of vi , a, t d= vit + ½ at

Displacement (d) in terms of vi , a, t d= vit + ½ at 2

How do we derive d= vit + ½ at 2 ? Hint: Start with

How do we derive d= vit + ½ at 2 ? Hint: Start with d= ½ (vf + vi)t and then substitute for vf that vf = vi+at.

• Final Velocity in terms of vi, a, d vf 2 = vi

• Final Velocity in terms of vi, a, d vf 2 = vi 2 + 2 ad

How do we derive vf 2 = vi 2 + 2 ad ? n

How do we derive vf 2 = vi 2 + 2 ad ? n Hint: Start with d= ½ (vf + vi)t and then substitute for t = (vf – vi) /a.

Equations of Motion for Uniform Accelerated Motion vf= vi+ at vavg = ½ (vf

Equations of Motion for Uniform Accelerated Motion vf= vi+ at vavg = ½ (vf +vi) d= ½ (vf + vi)t d= vit + ½ at 2 vf 2 = vi 2 + 2 ad d is the displacement (or Δd) n Assume that ti=0 n

Solving Kinematics Problems Draw a labeled vector diagram showing the positive and negative direction.

Solving Kinematics Problems Draw a labeled vector diagram showing the positive and negative direction. n Make a list of the givens (include signs as needed) and unkown. n Decide what equation(s) you should use. n Write the equation(s) and solve for the unknown. Always include units in your first substitution and in your final answer. n

Problem 1 A rocket travelling at +95 m/s is accelerated uniformly to +150 m/s

Problem 1 A rocket travelling at +95 m/s is accelerated uniformly to +150 m/s in 10 s. What is the displacement? Answer: 1, 225. m

Problem 2 An airplane has a minimum take off velocity of 80 m/s. How

Problem 2 An airplane has a minimum take off velocity of 80 m/s. How long should the runway be, if the airplane can accelerate on the ground at 3 m/s 2 ? Answer: 1, 067 m

Problem 3 1. 2. An airplane landing at +100 m/s, comes to a stop

Problem 3 1. 2. An airplane landing at +100 m/s, comes to a stop in 30 s. What is the acceleration? How far did it travel on the runway before it stopped? Answer: -3. 3 m/s 2, 1, 515 m

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