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Velocity starting with the position equation

Enunciado: If a body moves according to the following equation: r (t) → = (4 · t + t 2) · i → + 4 · t · j → m Calculate its instantaneous velocity at time t=1 s. Español Idioma Inglés Solución: Data r (t) → = (4 · t + t 2) · i → + 4 · ...

A particle in motion

Enunciado: The position of a certain particle depends on time according to the equation x (t) = t 2- 5 t + 1. 2 , where x is expressed in meters and t in seconds. You are asked to: Determine the displacement and the average velocity during the interval ...

Average speed in a circular trajectory

Enunciado: A body is in a circular track like the one in the figure. If the radius is 80 m, calculate: The average speed between points A and B, if the body takes 13 seconds to go from one point to the other The average speed between points A and C if a ...

Average speed of the Moon

Enunciado: Knowing that the Moon takes 28 days to make one complete revolution around the Earth, calculate its average speed. Datum: Consider the trajectory of the Moon as circular with a radius of 384,000 Km. Español Idioma Inglés Solución: First, we c ...

Average speed in a full circle

Enunciado: A body does a full circle of 4-meter radius in 1.5 seconds. Calculate: a) the average speed. b) the average velocity. Español Idioma Inglés Solución: Question a) Data Travels a full circumference of radius r=4m. Elapsed time Δt=1,5 s. Δt=1,5 ...

Speed as a function of distance traveled

Enunciado: Knowing that the distance a body travels as a function of time is given by the following equation: S (t) = t 2 + 5 · t + 1 Calculate: a) The average speed during the first 3 seconds. b) The instantaneous speed of the body. Español Idioma Inglé ...

Acceleration graphs

Enunciado: Given the following graphs that show the variation of the speed with time of three different bodies, answer the following questions: a) Which case has the fastest variation of the speed? b) What does the slope represent in each one of the 3 ca ...

Acceleration in a basketball throw

Enunciado: A basketball player throws the ball with a velocity of v → 1 =- 2 · i → + j → m / s, with such bad luck that it bounces off the board with a velocity v → 2 = 15 · i → + 3 · j → m / s. Calculate the average acceleration knowing that the i ...

Acceleration of a meteorite

Enunciado: A meteorite moves through space with a velocity v⃗(t) = (1+4·t) i⃗+t 2 j⃗ m. Calculate a) Its average acceleration between the times t 1 =2 s and t 2 = 4 s. b) Its acceleration at t 3 = 6 s. Español Idioma Inglés Solución: Question a) Data v⃗ ...

Magnitude of the tangential acceleration

Enunciado: Knowing that the magnitude of the velocity of a body in S.I. units is: v = 7 + 2 · t + 3 · t 2 Calculate the magnitude of the tangential acceleration. Español Idioma Inglés Solución: Knowing that the tangential acceleration is obtained by the ...