QUESTION Suppose the velocity v, of the car at any time t is given by the equation: Vx = 30m/s + (0.75m/s*)t3 Find the average acceleration in m/s2 of the car in the time interval between t 2.0 s and t, = 3.0 s. %3D
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- A runner is moving with a speed of 2.68[m/s]. How long will it take the runner to complete a 5.0[km] race? Express your answer in seconds. Ignore the time it takes to reach this speed, and assume the runner is always at this speed.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.A person standing at the edge of a cliff throws a rock upward from a height of 350ft above ground level with an initial velocity of 65ft/s. What is the velocity of impact when the rock reaches the bottom of the cliff? Round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to two decimal places. (Hint: Use h(t)=−16t2+65t+350 as the position function, where hh is in feet, tt in seconds. Ignore air resistance.)
- My pug/bulldog mix, Georgia, who is blind and deaf, gets a whiff of her dinner. As soon as it registers to her that it's dinnertime, she runs 4.12 meters from the middle of our living room to our kitchen, where she is satiated with her grub. If it takes her 4.45 s to get to the kitchen, what was her speed in m/s to the nearest hundredth?A car can be braked to a stop from the autobahn-likespeed of 200 km/h in 170 m. Assuming the acceleration is constant,find its magnitude in (a) SI units and (b) in terms of g. (c) How muchtime Tb is required for the braking? Your reaction time Tr is the timeyou require to perceive an emergency, move your foot to the brake,and begin the braking. If Tr = 400 ms, then (d) what is Tb in terms ofTr, and (e) is most of the full time required to stop spent in reactingor braking? Dark sunglasses delay the visual signals sent from theeyes to the visual cortex in the brain, increasing Tr. (f) In the extremecase in which Tr is increased by 100 ms, how much farther doesthe car travel during your reaction time?Calculate the height (in m) of a cliff if it takes 2.27 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.07 m/s. (b) How long (in s) would it take to reach the ground if it is thrown straight down with the same speed?
- . A body has an initial velocity of 45km/h and is accelerated uniformly at2m/s2 until its velocity is 72km/h after which is brought to a rest with auniform retardation, if the total remaining time is 12 seconds;i. Sketch the velocity-time graphii. Show that, the total distance covered can be determinedA car comes to a complete stop from an initial speed of 60 mi / hr in a distance of 200 ft. With the same constant acceleration, what would be the stopping distance s from an initial speed of 55 mi / hr?Dr. John Paul Stapp was a U.S. Air Force officer who studied the effects of extreme deceleration 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 the magnitude of his average acceleration during the first part of his motion. Express your answer in multiples of g by taking its ratio to 9.80 m/s2. calculate the magnitude his average deceleration during the second part of his motion. Express your answer in multiples of g by taking its ratio to 9.80 m/s2.
- Professional Application Dr. John Paul Stapp was U.S. Air Force officer who studied the effects of extreme deceleration 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 and (b) deceleration. Express each in multiples g (9.80 m/s) of by taking its ratio to the acceleration of gravity.The velocity of a particle traveling in a straight line is given by v = (6t - 3t^2) m/s, where t is in seconds. If s = 0 when t = 0, determine the particle’s deceleration and position when t = 3 s. How far has the particle traveled during the 3-s time interval, and what is its averagespeed?In problem 11, if the dragstrip is ¼ mile, or 402.3 meters long, at the acceleration of 24.1 m/s2, what is the time that thedragster records for his or her quarter mile run to two decimal places assuming uniform acceleration during the entirelength of the track? What was the dragster’s final velocity in miles per hour (two decimal places) when it crossed thefinish line and deployed its parachute?