A particle is moving along a straight line in rectilinear motion. If the velocity of the particle is v(t)=-16t² +96t, find the total distance traveld by the object over the time period [0, 10].

The LORAN (LOng RAnge Navigation) radio navigation system was widely used until the 1990s when it was superseded by the GPS system. In the LORAN system, two radio stations located at A and B transmit simultaneous signals to a ship or an aircraft located at P. The onboard computer converts the time difference in receiving these signals into a distance difference |PA| = |PB|, and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure). coastline 430 mi transmitting stations P B Suppose that station B is located 430 mi due east of station A on a coastline. A ship received the signal from B 1,200 microseconds (us) before it received the signal from A. (a) Assuming that radio signals travel at a speed of 980 ft/µs, find an equation of the hyperbola on which the ship lies. (Use x as the axis along the coastline, and center your coordinate system between A and B. Values should be in miles.) (b) If the ship is due north of B,…

The position F of a particle moving in an xy plane is given by: F=(200*-5.002)i + (6.00–7.00*)} with F in meters and t in seconds. (Note that this is an example where the units for the coefficients are ignored – don't let this distract you!) In unit vector notation, calculate: а). г b). й с). а for time t= 2.00 s. %3D d). What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t= 2.00 s?

A rodeo horse is running around a corral at a speed of 300 ft/s. Let x(t) be the distance of the horse from the third barrel and y(t) his distance from the fourth. (see figure; note that the distance between barrels is 900 řt). At what rate is the horse's distance from the fourth barrel changing at the instant when he is 200 ft from the third? 2 1 3 4

The instantaneous speed of a particle moving along one straight line isv(t) = ate−5t, where the speed v is measured in meters per second, the time t is measured in seconds, and the magnitude of the constant a is measured in meters per second squared. What is its maximum speed, expressed as a multiple of a? (Do not include units in your answer.)

An experimentalist in a laboratory finds that a particle has a helical path. The position of this particle in the laboratory frme is given by r(t)= R cos(wt)i + R sin(wt)j + vztk R,vz, and w are constants. A moving frame has velocity (Vm)L= vzk relative to the laboratory frame. In vector form: A)What is the path of the partical in the moving frame? B)what is the velocity of the particle as a function of time relative to the moving frame? C)What is the acceleration of the particle in each frame? D)How should the accelerartion in each frame be realted?Does your answer to part c make sense?

A spacecraft starts from rest, and makes a journey to a destination 389000 km from its starting point. It does so by accelerating at a constant rate of 9.79 m/s^2 up to the midpoint of the journey, and then decelerates at the same constant rate of 9.79 m/s^2 for the second half of the journey, ending at rest. How long did the entire journey take?     11 hr 2 min     5 hr 31 min     3 hr 30 min     2 hr 29 min

A particle is moving on xy plane, with x=15sin(2t), and y = 20cos(2t) Find the magnitude of the velocity as a function of time

An object is moving in a circle of radius 10 cm centered on the origin in the xy-plane at a constant speed of 5 m/s. (a) Express the motion of the object as a vector that depends on time, i.e. find F(t).

Just need help with part B