Statics and Dynamics Equations of Motion

s = displacement t = time u = initial velocity v = final velocity a = acceleration What are the variables?

What are the equations? (km) Example:

You often see this equation written as: Example: A car accelerates from rest to 22.2 m s -1 in 4 seconds. What is its acceleration? u = 0 ms -1 v = 22.2 ms -1 t = 4 s

The other equations of motion are:

How to use them: 1.Ima Hurryin approaches a stoplight in her car which is moving with a velocity of 30.0 m s -1. The light turns orange, Ima applies the brakes and skids to a stop. If Ima's acceleration is –8.00 m s -2, determine the displacement of the car during the skidding process. Solution u=30m/s v=0 m/s u = 30 ms -1 v = 0 ms -1 a = -8 ms -2 s = ? v 2 = u 2 + 2as 0 2 = (-8)s 0 = s 16s = 900 s = 900 16 s = 56.3 (Round to 3 sig figs) Therefore, the car skids for 56.3 m. Check your answer by substituting it back into the equation. Check this sounds reasonable

How to use them: 2.Ben Rushin is waiting at a stoplight in his car. When the light turns green, Ben accelerates from rest at a rate of a 6.00 m/s 2 for an interval of 4.10 seconds. Determine the displacement of Ben's car during this time period. Solution u = 0 ms -1 a = 6 ms -2 s = ? (Round to 3 sig figs) Therefore, the displacement of Ben’s car is 50.4m. Check your answer by substituting it back into the equation. t = 4.10 s s = s = 50.4 m u=0m/s Check this sounds reasonable

Vertical Motion For an object in free fall: o Acceleration is always -9.8 ms -2. That is, 9.8 ms -2 in the downward direction. o If an object is dropped from an elevated height, its initial velocity is 0 ms -1. o If an object is projected upwards in a vertical direction, it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 ms -1. o If an object is projected upwards in a vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity it has when it returns to the same height.

3.Luke Autbeloe drops a pile of roof tiles from the top of a roof located 8.52 metres above the ground. Determine the time required for the tiles to reach the ground. Solution u = 0m/s u = 0 ms -1 s = m a = -9.8 ms -2 t = ? Therefore, the tiles will take 1.32 seconds to reach the ground.

4.Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Solution v = 0m/s u = 26.2 m/s u = 26.2 ms -1 v = 0 ms -1 a = -9.8 ms -2 s = ? Therefore, the vase will reach a height of 35.0 metres.