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Exam_1_09s

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Physics 130 Exam 1 Short Answer. Please answer all of the short answer questions. 1. A new group is trying to shatter the land speed record. Their goal is to go 1000 mi/hr. How fast is this in m/s? v = 1000 mi hr 1600 km 1 mi 1 hr 3600 s = 444.4 m / s 2. You have a leaky faucet. If it drips once per second, estimate how what volume water you will have wasted in 1 year. If the density of water is 1000 kg/m 3 , what mass of water is this? Estimated that each droplet is 1/8 cm 3 . V = 1/ 8 cm 3 s 3600 s 1 hr 24 hrs 1 day 365 days 1 yr 1 yr = 3.94 × 10 6 cm 3 = 3.94 × 10 6 cm 3 1 m 100 cm 3 = 3.94 m 3 m = 1000 kg m 3 3.94 m 3 = 3940 kg 3. If the vehicle that is attempting to break the land speed record by reaching 1000 mi/hr achieves a constant acceleration of 1.5 g’s, how long will it take to reach its design speed of 1000 mi/hr? Assume it started from rest. x i = 0 x f = ? v i = 0 m / s v f = 444.4 m / s a = 1.5 g t = ? v f = v i + at v f = 0 + 1.5 gt t = v f 1.5 g = 444.4 m / s 1.5 9.8 m / s 2 = 30.23 s 4. How far will you need to stop your vehicle if it is going 1000 mi/hr? Assume that the vehicle can decelerate with magnitude 0.5 g.

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x i = 0 x f = ? v i = 444.4 m / s v f = 0 m / s a = 0.5 g t = ? v f 2 = v i 2 + 2 a ( x f x i ) 0 = v i 2 + 2( 0.5 g )( x f 0) x f = v i 2 2(0.5 g ) = 20,152.2 m 5. The position of a particle is given by x ( t ) = 2 + 5 t 2 + 10 t 3 Find the average velocity over the interval 0 s to 2 s, the instantaneous velocity at 1s, and the instantaneous acceleration at 1s. x ( t ) = 2 + 5 t 2 + 10 t 3 x (0) = 2 m x (2) = 102 m v avg = x (2) x (0) 2 s = 50 m / s x ( t ) = 2 + 5 t 2 + 10 t 3 v ( t ) = 10 t + 30 t 2 v (1) = 40 m / s 6. Consider vectors a = 4 ˆ i + 3 ˆ j and b = 13 ˆ i + 5 ˆ j Compute the magnitude and direction of BOTH a and b . Compute the result of a b , a b ,
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