Question

1. Which of the following equations are dimensionally correct? a.) V = V1 + ax (10p) b.) y = (2m)cos(kx), where k = 2m-1 (10p) 2. Given the vectors A = 2.001 + 6.00j andB = 3.00i + 2.00j. a.) draw the vector sum C = A + B and the vector differenceD = A - B. (10p) b.) Calculate C and D, first in terms of unit vectors and then in terms of polar coordinates, with angles measured with respect to the +x axis. (15p) 3. Consider the three displacement vectors A = (31 - 31) m, B = (i - 47) m, and C = (-21 +57) m. Use the component method to determine a.) the magnitude and direction of the vector D = A - B + C, (12p) b.) the magnitude and direction of E = A - B + C. (13p) 4. A velocity-time graph for an object moving along the x axis is shown in Figure 1. a.) Plot a graph of the acceleration versus time. (10p) b.) Determine the average acceleration of the object in the time intervals t = 5.00 s to t = 15.0 s and t = 0 to t=20.0 s. (15p) (m/s) 1 2 (8) 5 10 15 -2 Figure 1 5. An object moves along the x axis according to the equation x(t) = (3.0062 - 2.00t + 3.00) m. Determine a.) the average speed between t = 2.00 s and t = 3.00 s, (5p) b.) the instantaneous speed at t = 2.00 s and at t = 3.00 s, (5p) c.) the average acceleration between t = 2.00 s and t = 3.00 s, and (10p) d.) the instantaneous acceleration at t = 2.00 s and t = 3.00 s. (10p)

Answer 1

is dimensiona 1 nally The following equan equation is = (2 m) cos(kx) where, k = 2ml correct - b. Y

(2) Given, À =2 ↑ + 6 ř = 39+ 2 () = À & B = (21+55)+ ( 39 +23) - 5 ↑ + 8 i Y Ald D = ÅR = (20 +67) - (31 + 25) - ît 4 х (b) = 5 ņ + 8 = -9 + 4) Magnitude of ?, = 58° D lil= I 8 p 87 = 9.43 tan' ( 8 ) in polar con ordinate is ( 9.13,582 vector i

For the vector 5, = J (13 + 4 tam' (- 7 > 4.12 -76 180-76 = 10.40 Polar coordinate of it is ( 4.12, 104) m À = 137 - 37 ) B - (1-15) - 1-29 +59) To m ca B = A - B + P 3î - 37 - î + 47 - rî +57 of + 6 6 19 m The magnitude of rector I is om anis + Y the direction along (6) E = -5+7 = 63 Magnitude: Direction: along 6 M tt anis.

4.6) Acceleration vs time gosph a(m/sy b 2 +13) 0 is 2 -4 - 6 The average acceleration acceleration of the object in the time interval 4-505.0s to t=15 s is- 1.6 +1.6 I als Aar = The average acceleration in the time interval tso to t=205 is o
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