Friday, September 17th 2010

Grade 12 Mechanics Unit: Acceleration Test (Answers):

1) Step 1: Square both sides of the equation
V2² = V1² + 2V1at + a²t²
Step 2: Factor out 2a from the last two terms
V2² = V1² + 2a(V1t + ½at²)
Step 3: Substitute a term in the equation given in step 2
V2² = V1² + 2ad
Step 4: The equation is _____
V2² = V1² + 2ad

2) V1 = 40.0km/h ÷ 3.6 = 11.11m/s
a = -2.3m/s²
t = 2.7s
d = ?
V2 = ?

2a) d = V1t + ½at²
d = (11.11)(2.7) + ½(-2.3)(2.7)²
d = 21.6m

2b) V2 = V1 + at
V2 = 11.11 + (-2.3)(2.7)
V2 = 4.89m/s

3) V1 = 0m/s
a = 0.300m/s²
d = 25.0m
V2 = ?

V2² = V1² + 2ad
V2² = 0² + 2(0.300)(25.0)
V2² = 15
V2 = 3.87m/s

4) motorist = 80.0km/h(W)
police car = 95.0 km/h(W)

4a) motorist - police car
80.0 - 95.0 = 15km/h(E)

4b) police car - motorist
95.0 - 80.0 = 15km/h(W)

5) airplane's airspeed = 2.0 x 10²km/h(E)
approching destination = 15°(N of E)

5a) tan15° = 200 ÷ wind speed
wind speed = 200 ÷ tan15°
wind speed = 53.6km/h

5b) c² = a² + b²
speed approaching destination = (2.0 x 10²)² + (53.6)²
speed approaching destination = 207km/h

6) V1 = 25m/s
t = 1.45s
a = -8.5m/s²
V2 = 0m/s
d = ?

reacting to child and applying the brakes:
d = Vt
d = (25)(0.45)
d = 11.25m
after applying the brakes:
V2² = V1² + 2ad
d = V2² - V1² ÷ 2a
d = (0)² - (25)² ÷ 2(-8.5)
d = 36.76m
total distance = 11.25m + 36.76m = 48.0m

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Equilibrium: When an object has zero acceleration, meaning that the object is at rest or moving at constant velocity
Free Body Diagram: A drawing that represents the object and the forces acting on it

Steps to Drawing a Free Body Diagram:

1) Focus on the object you will be studying. If there is more than one object in the drawing, do each seperately.
2) Begin drawing the free body diagram by looking at only the desired object. The drawing will show where forces are applied to the object, so draw those forces on your free body diagram in exactly the same direction thats shown on the drawing.
3) Draw x and y axes on your free body diagram so you will be able to analyse the diagram. Try to draw your axes so that as many forces as possible are close or directly on the axes. It will help when calculating.
4)When the situation is equilibrium, make sure that the x and y components of the forces will be equal to zero when added.
5) Finally, solve for the unknown quantities.

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In class we received the 'Grade 12 Physics: Dynamics Unit' booklet, some of us recieved this booklet after finishing the Acceleration Test on Thursday. We read pg.1, completed pg.14, and completed #1 on pg.16. For homework we were assigned pg.12 & 13 (Free Body Diagrams) and #2-5 on pg.16 & 17 (Static Equilibrium Problems).