Question

Рівняння руху велосипедиста, який рухається вздовж осі OX, має вигляд х=1000-2t . Знайдіть координату тіла та модуль його переміщення через 5 хв після початку спостереження.

Answer 1

Equation of Motion for the Cyclist

The equation of motion for the cyclist moving along the x-axis is given by x = 1000 - 2t, where x represents the position of the cyclist along the x-axis and t represents time in seconds.

Finding the Coordinate of the Cyclist after 5 minutes

To find the coordinate of the cyclist after 5 minutes (300 seconds) from the start of observation, we can substitute t = 300 into the equation x = 1000 - 2t and solve for x:

x = 1000 - 2(300) x = 1000 - 600 x = 400

Therefore, the coordinate of the cyclist after 5 minutes is x = 400.

Finding the Magnitude of Displacement

The magnitude of displacement represents the shortest distance between the initial and final positions of the cyclist. In this case, we can calculate the magnitude of displacement by finding the absolute difference between the initial position (t = 0) and the final position (t = 300).

Substituting t = 0 into the equation x = 1000 - 2t, we find the initial position:

x = 1000 - 2(0) x = 1000

Substituting t = 300 into the equation x = 1000 - 2t, we find the final position:

x = 1000 - 2(300) x = 1000 - 600 x = 400

The magnitude of displacement is then given by the absolute difference between the initial and final positions:

Magnitude of Displacement = |Final Position - Initial Position| Magnitude of Displacement = |400 - 1000| Magnitude of Displacement = |-600| Magnitude of Displacement = 600

Therefore, the magnitude of displacement of the cyclist after 5 minutes is 600 units.

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