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Test Your Skill

1. A motorcycle can accelerate from 0 to 60 mph in 5.7 seconds. Determine the average rate of acceleration.
2. A car is traveling at 45 mph and a motorcycle is traveling at 80 mph in the opposite direction. The distance between them is 650 feet. If they both maintain constant speed, how much time will elapse before they collide?

Answers

1. First convert the final speed of the motorcycle to feet per second (fps).
   (60)(22)/15 = 88 fps
   The average rate of acceleration equals the change in velocity divided by elapsed time. The acceleration test took 5.7 seconds. Using the equation:
   a = V/t = 88/5.7 = 15.4 feet per second per second
   
   We may also convert the answer to g's by dividing by the acceleration of gravity (32.2 feet per second per second)
   15.4/32.2 = .48 g's
2. First we must convert the speeds of the vehicles to feet per second:
   Car: (45)(22)/15 = 66 fps
   Motorcycle: (80)(22)/15 = 117.3 fps
   
   The closing velocity is the sum of the two vehicle velocities:
   V = V_mc+V_car = 117.3+66 = 183.3 fps
   
   The time required to cover the 650 feet is the distance divided by the closing velocity:
   t = d/V = 650/183.3 = approx. 3.5 seconds

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