05 Midterm 1 Solutions Ch. 1-3

05 Midterm 1 Solutions Ch. 1-3 - 1. Units and Vectors (8...

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Version A 1. Units and Vectors (8 points) a. In SI units, energies are measured in units called Joules, where 1.00 Joule = 1.00 kg m 2 /s 2 . An alternative unit of energy is the Dyne: 1.00 Dyne = 1.00 g cm 2 /s 2 . How many Dynes are there in 2.50 Joules? 2 32 22 7 10 g 10 cm 1Dyne 2.50 kg m /s 2.50 10 Dynes kg m 1.00 g cm /s ⎛⎞ ×× × = × ⎜⎟ ⎝⎠ A: 2.50×10 7 Dynes B: 4.25×10 7 Dynes C: 6.50×10 7 Dynes D: 6.50×10 7 Dynes b. The vector A has a magnitude of 5.00 m, and is oriented at an angle of +30.0° from the x axis. Find a vector B (in the form B x i + B y j ) so that A B has a magnitude of 4.00 m and is oriented in the direction of the positive y axis. () 4.00 m 5.00 m cos 5.00 m sin 0 5.00 m cos 4.33 m 4.00 m 5.00 m sin 4.00 m 1.50 m 4.33 m 1.50 m y x y xx x yy y yyy ABC j Cj A A CA B BA B C Bi j θ −==+ = = = == − == = + =−= = =+ +− GG G G A: B x = 4.33 m, B y = -1.50 m B: B x = 4.60 m, B y = +0.857 m C: B x = 6.58 m, B y = +0.394 m D: B x = 0.867 m, B y = -2.50 m
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Version A 2. Velocity and Speed (8 points) a. A object moves 90.0 m west in 4.00 s, stops for 3.50 s, and then continues south for 60.0 m over 7.00 s. Find the object’s average speed. Distance traveled: D = 90.0 + 60.0 m = 150. m Time interval Δ t = 4.00 + 3.50 + 7.00 s = 14.5 s Average speed v = D/ Δ t = 10.3 m/s A: 10.3 m/s B: 5.00 m/s C: 10.0 m/s D: 7.89 m/s b. Find the object’s average velocity. Velocity is a vector, but the TA who graded this problem gave full credit for the magnitude of the velocity… () 22 90.0 m 60.0 m 6.21m/s 4.14 m/s 6.21m/s 4.14 m/s 7.46 m/s x y xy x y x v t y v t vi j vv v Δ=− Δ == Δ Δ Δ =− +− =+ = GG G G If you only want the magnitude of the velocity, an alternative solution is to calculate the magnitude of the displacement, ()() rxy Δ= Δ +Δ ; then the magnitude of the average velocity is Δ r/ Δ t. A: |v| = 7.46 m/s B: |v| = 3.57 m/s C: |v| = 7.52 m/s D: |v| = 5.69 m/s
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Version A 3. Acceleration (8 points) a. If a car accelerates from rest at 2.50 m/s 2 , what will its velocity be after it has traveled 50.0 m? () 22 2 2 2 0 2.50 m/s 50.0 m 2 2.50 m/s 50.0 m 2 2.50 m/s 50.0 m 15.8 m/s fi i f f vv a x v a x v v =+ Δ = = Δ= = == A: v = 15.8 m/s B: v = 22.1 m/s C: v = 15.5 m/s D: v = 10.0 m/s
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Version A b. You drive into a narrow tunnel at a speed of 30.0 m/s, and see a slow-moving vehicle 60.0 m ahead of you, moving in the same direction with a constant speed of 12.0 m/s. Find the (negative) acceleration your brakes must provide so that you can just barely avoid a collision, and sketch the position vs. time curves of your car and the other one in this case, labeling which curve corresponds to which vehicle.
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This note was uploaded on 09/08/2008 for the course PHYS 3A taught by Professor Casper during the Fall '07 term at UC Irvine.

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05 Midterm 1 Solutions Ch. 1-3 - 1. Units and Vectors (8...

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