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Equations of Uniform Accelerated Motion

Equations of Uniform Accelerated Motion. Physics Mrs. Coyle. Average Velocity . v = ½ (v f +v i ). . Displacement in terms of Average Velocity and Time . d= v t d= ½ (v f + v i ) t. . How do we derive d= ½ (v f + v i )t from the graph?. v f. Velocity (m/s). v i. o. Time (s).

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Equations of Uniform Accelerated Motion

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  1. Equations of Uniform Accelerated Motion Physics Mrs. Coyle

  2. Average Velocity v = ½ (vf +vi) 

  3. Displacement in terms of Average Velocity and Time d= v t d= ½ (vf + vi) t 

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

  5. Displacement (d) in terms of vi , a, t d= vit + ½ at2

  6. How do we derive d= vit + ½ at2 ? Hint: Start with d= ½ (vf + vi)t and then substitute for vf that vf = vi+at.

  7. Final Velocity in terms of vi, a, d vf2 = vi2 + 2ad

  8. How do we derive vf2 = vi2 + 2ad ? • Hint: Start with d= ½ (vf + vi)t and then substitute for t= (vf – vi) /a .

  9. Equations of Motion for Uniform Accelerated Motion vf= vi+ at vavg = ½ (vf +vi) d= ½ (vf + vi)t d= vit + ½ at2 vf2 = vi2 + 2ad • d is the displacement (or Δd) • Assume that ti=0

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

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

  12. Problem 2 An airplane has a minimum take off velocity of 80m/s. How long should the runway be, if the airplane can accelerate on the ground at 3m/s2 ? Answer: 1,067m

  13. Problem 3 An airplane landing at +100m/s, comes to a stop in 30s. • What is the acceleration? • How far did it travel on the runway before it stopped? Answer: -3.3m/s2, 1,515m

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