4.53 B. 80.00 C. I.I +21.6 112.3 3.70 33.7 SSM Example 1-4 1-5 Dimensional analysis is a powerful way to check the results of a physics calculation 41. One equation that describes motion of an object is 5 xat+vot +xo, where x is the position of the object, a is ai the acceleration, t is time, vo is the initial speed, and xo is the initial position. Show that the dimensions in the equation are consistent. 42. . One equation that describes motion of an object is x ut t xo, where x is the position of the object, v is its speed, t is time, and xo is the initial position. Show that the dimensions inx bl the equation are consistent. SSM 43. . The motion of a vibrating system is described by y(x, t) A e-at sin(kx-wt). Find the SI units for k, a, and α. 44. . The kinetic energy of a particle is K m2, where m is the mass of the particle and v is its speed. Show that 1 joule (J), the SI unit of energy, is equivalent to 1 kg m2/s2. 45. .The period T of a simple pendulum, the time for one complete oscillation, is given by T 2TV(L/8), where L is the per length of the pendulum and g is the acceleration due to gravity Show that the dimensions in the equation are consistent obj in a 46 . Which of the following could be correct based on a body dimensional analysis? A. The volume flow rate is 64 m3/s B. The height of the Transamerica building is 332 m2. C. The time required for a fortnight is 66 m/s. D. The speed of the train is 9.8 m/s E. The weight of a standard kilogram mass is 2.2 lb F. The density of gold is 19.3 kg/m2. SSM to tra speed and in nifica amoun mass h in m General Problems 47. You hire a printer to print concert tickets. He delivers them in circular rolls labeled as 1000 tickets each. You want to check the number of tickets in each roll without counting thousands of tickets. You decide to do it by measuring the diameter of the rolls f th an

A car is traveling at a speed of 33 m/s. (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h speed limit?

After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by v=1.2i9.8tj where v is in meters per second and t is in seconds. The balls displacement away from the edge of the table, during the time interval of 0.380 s for which the ball is in flight, is given by r=00.3803vdt To perform the integral, you can use the calculus theorem [A+Bf(x)]dx=Adx+Bf(x)dx You can think of the units and unit vectors as constants, represented by A and B. Perform the integration to calculate the displacement of the ball from the edge of the table at 0.380 s.

A garden snail named Archie, owned by Carl Branhorn of Pott Row, England, covered a 33-cm course in 2.0 min at the 1995 World Snail Racing Championships, held in Longhan, England (Fig. P1.13). Determine Archies average speed Sav = d/t in the appropriate SI units.