A motorcyclist traveling at 30.7 km/h accelerates after passing a sign post marking the city limits . If it takes 4.9 seconds for the motorcyclist to reach 120 km/h how far has he traveled (in meters) past the sign post ?
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initial velocity , u = 30.7 km/h = 30.7 × 5/18
= 153.5/18 = 8.52 m/s
final velocity, v = 120 km/h = 120 × 5/18
= 33.33 m/s
now, v = u + at [ formula ]
33.33 = 8.52 + a × 4.9
33.33 - 8.52 = 4.9a
a = 5.06 m/s
now, v² = u² + 2as [ formula ]
(33.33)² = (8.52)² + 2 × 5.06 × s
s = {33.33² - 8.52² }/2 × 5.06
= 102.59 m
he travelled 102.59 m past the sign post.
= 153.5/18 = 8.52 m/s
final velocity, v = 120 km/h = 120 × 5/18
= 33.33 m/s
now, v = u + at [ formula ]
33.33 = 8.52 + a × 4.9
33.33 - 8.52 = 4.9a
a = 5.06 m/s
now, v² = u² + 2as [ formula ]
(33.33)² = (8.52)² + 2 × 5.06 × s
s = {33.33² - 8.52² }/2 × 5.06
= 102.59 m
he travelled 102.59 m past the sign post.
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