Chapter 5: Exercises with Solutions

Section 5.5Motionv = v 0 + at= 0 m (s + 15.8 m/s )× 180 ss= 0 m s + 2844m s= 2844 m/s25. We are trying to solve for v, so v = v 0 + at is the formula we want to use. Butnotice that the acceleration a and initial speed v 0 are given in units involving seconds,while time t is given as 1 minute. We must first make the units match, so convertt = 1 min = 60s.The initial speed is v 0 = 20 ft/s and the acceleration is a = 32 ft/s 2 . Now plug intothe formula.v = v 0 + at= 20 ft (s + 32 ft/s )× 60 ss= 20 ft (s + 1920 ft )s= 1940 ft/s27. We are given v 0 = 100 m/s, a = −9.8 m/s 2 and are asked to find t when the ballhas reached maximum height. The ball will reach its maximum when v = 0 m/s. So,we are really given v, v 0 , and a and asked to find t. First, solve the formula for t.v = v 0 + atv − v 0 = atAnd now plug in what we know.at = v − v 0t = v − v 0at = v − v 0a0 m/s − 100 m/s=−9.8 (m/s)/s≈ 10.2 m/s ×sm/s= 10.2 sVersion: Fall 2007