Chapter 2, Problem 8Q

A particle is moving along a line with position given by s(t)=t3−(9/2(t2 ))+6t−5 measured in meters, with t≥0 measured in minutes, and the positive direction meaning forward. a) Find the equation for the velocity at time t. Give units, and find times the times the particle is moving forward. b) Find the equation for the velocity at time t. Give units, and find times the times the particle is moving backwards. c) Find the total distance travelled by the particle. d) Find the equation of the acceleration at time t. Give the units, and find the times when the velocity of the particle is not changing. e) Find the displacement.

Una partícula parte de origen en t = 0 con una velocidad de 6.0i m / s y se mueve en el plano xy con una aceleración constante de (–2.0i + 4.0j) m / s2. En el instante en que la partícula alcanza su máxima componente en x positiva, ¿qué tan lejos está del origen?

In certain physical models, the nonhomogeneous term, or forcing term, g(t) in the equation ay" + by' + cy = g(t) may not be continuous, but have a jump discontinuity. If this occurs, a reasonable solution can still be obtained using the following procedure. Consider the following initial value problem. 240 if 0sts7T/6 y" + 4y' + 40y = g(t); y(0) = 0, y'(0) = 0, where g(t) = . if t> 7x/6 Complete parts (a) through (c) below. (a) Find a solution to the initial value problem for 0 sts 71/6. The solution for 0sts 7n/6 is y(t) = - 6 e -21 *cos 6t - 2 e - 2t sin 6t + 6 (Type an equation.) (b) Find a general solution for t> 71/6. The general solution for t> 7x/6 is y(t) = C, e-2 cos 6t + C, e -2t sin 6t (Type an equation. Do not use d. D. e, E, i, or I as arbitrary constants since these letters already have defined meanings.) (c) Now choose the constants in the general solution from part (b) so that the solution from part (a) and the solution from part (b) agree, together with their first…

What is the sum of the following numbers, including significant digits and uncertainties: 13.5 + 0.3 plus 5.1 ± 0.2 O 19 + 0.5 O 18.6 ± 1 O 18.6 ± 0.5 O 19 ±1

For A= 3î + 4ĵ − 3,  B= -2î + ĵ + , and  C= 2ĵ − 5, find C · (A −B ).

Problem 4: Arunner runs around a circular track. He completes one lap at a time of t= 386 s at a constant speed of v = 4.7 m/s. Randomized Variables t = 386 s v = 4.7 m/s What is the radius, r in meters, of the track? a()7 8 9 E A 4 5 2 3 sin() cos() tan() HOME cotan() asin() acos() 6 atan() acotan() sinh() 1 cosh() tanh() cotanh() END O Degrees O Radians VOl BACKSPACE DEL CLEAR Submit I give up! Hint Feedback What was the runners centripetal acceleration, a, in m/s, during the run?

A bird flies a distance of d = 150±3 m during a time t = 20.0±1.0 s. The average speed of the bird is v = d/t = 7.5 m/s. What is the uncertainty of v?

The spectrum of a sun-like star is monitored and it is noticed that a spectral absorption line of wavelength A = 589 nm shifts periodically with a period equal to 10 days. The amplitude of the shift AX = ±1 × 10¬4 nm. The sun-like star has a mass M, = 2 × 1030 kg. Assuming that the periodic shifting of spectral lines is due to an unseen orbiting planet, estimate its mass. Express your answer in Earth masses

a student measures the time of flight of a projectile and gets the following values (in seconds): 2.56, 2.58, 2.43, 2.58, 2.53, 2.42. What is the standard deviation of these values?