The position of an object in METERS is given by X(t) = B-t" + C-t %3D Find the Sl units of the constants "B" and "C B= 0.45 C = -1.0 x 10 Find the AVERAGE VELOCITY between tį 1.0s and t2 3.0s The instantaneous velocity is the of the position vector. The instantaneous velocity of our object is *t^ *B*t^ V(t) =
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- A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = t3 − 15t2 + 72t (a) Find the velocity at time t. v(t) = (b) What is the velocity after 5 s? v(5) = ft/s (c) When is the particle at rest? t = s (smaller value) t = s (larger value) (d) When is the particle moving in the positive direction? (Enter your answer in interval notation.) t (e) Find the total distance traveled during the first 8 s.ft(f) Find the acceleration at time t. a(t) = Find the acceleration after 5 s. a(5) = ft/s2 (g) Graph the position, velocity, and acceleration functions for the first 8 s. (h) When, for 0 ≤ t < ∞, is the particle speeding up? (Enter your answer in interval notation.) When, for 0 ≤ t < ∞, is it slowing down? (Enter your answer in interval notation.)A ball is thrown into the air by a baby alien on a planet in thesystem of Alpha Centauri with a velocity of 49 ft/s. Its heightin feet after t seconds is given by y = 49t −25t2.a.) Find the average velocity for the time period beginningwhen t0 = 1 second and lasting for the given time.t = .01 sec:t = .005 sec:t = .002 sec :t = .001 sec: b.) Estimate the instanteneous velocity when t = 1.An object's velocity as a function of time in one dimension is given by the expression; v(t) = 2.71t + 7.88 where are constants have proper SI Units. What is the object's velocity at t = 4.19 s?
- A rabbit is moving in the positive x - direction at 2.00 m/swhen it spots a predator and accelerates to a velocity of12.0 m/s along the negative y - axis, all in 1.50 s. Determine(a) the x - component and (b) the y - component of the rabbit’sacceleration.On a spacecraft two engines fire for a time of 532 s. One gives the craft an acceleration in the x direction of ax = 4.92 m/s2, while the other produces an acceleration in the y direction of ay = 7.16 m/s2. At the end of the firing period, the craft has velocity components of vx = 3743 m/s and vy = 4808 m/s. Calculate the magnitude of the initial velocity.A person skateboarding with a constant speed of 1.30 m>s releases a ball from a height of 1.25 m above the ground.Given that x0 = 0 and y0 = h = 1.25 m, find x and y for (a) t = 0.250 s and (b) t = 0.500 s. (c) Find the velocity, speed,and direction of motion of the ball at t = 0.500 s.
- 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.An object's position as a func of time is given by ; x(t) = - 200 (( t + 1 ) ^ - 1) + 6t^2. (Assume constants have proper SI Units) What are the object's instantaneous velocity at t = 3.00 seconds ? Answer = 48.5 m/sA classic physics problem states that if a projectile is shot vertically up into the air with an initial velocity of 146 feet per second from an initial height of 89 feet off the ground, then the height of the projectile, h, in feet, t seconds after it's shot is given by the equation: h=−16t2+146t+89h=-16t2+146t+89 Find the two points in time when the object is 126 feet above the ground (to one decimal places). Answer: The object is 126 feet off the ground at the following times: (Enter your two answers separated by a comma. Round to ONE decimal places.)
- Dr. John Paul Stapp was a U.S. Air Force officer who studied the effects of extreme acceleration on the human body. On December 10, 1954, Stapp rode a rocket sled, accelerating from rest to a top speed of 282 m/s (1015 km/h) in 5.00 s and was brought jarringly back to rest in only 1.40 s. Calculate his (a) acceleration in his direction of motion and (b) acceleration opposite to his direction of motion. Express each in multiples of g (9.80 m/s2) by taking its ratio to the acceleration of gravity.You encounter a moving walkway that is 81 m long and has a speed of 2.1 m/s relative to the ground. How long would it take you to cover the 81 m length of the walkway if, once you get on the walkway, you immediately turn around and start walking in the opposite direction with a speed of 1.6 m/s relative to the walkway? Express your answer using one significant figure.An object's velocity as a function of time in one dimension is given by the expression; v(t) = 3.8t + 6.68 where are constants have proper SI Units. At what time is the object's velocity 61.2 m/s?