Can you do all the questions and show your work.Thanks! Motion in one dimension

Question

Can you do all the questions and show your work.Thanks!

Motion in one dimension A particle's motion can be modeled by the equation x(t)-2t*-3t2 What is the magnitude of the displacement of the particle for the first 2 seconds of its motion? What is the average velocity for the first 2 seconds of its motion? Chart Title What is the average acceleration for the first 2 seconds of its motion? What is the instantancous velocity at t-4s? Kinematic Ken Runfast is the star of the cross-country team. During a recent morning run, Ken averaged a speed of 5.8 m/s for 12.9 minutes. Ken then averaged a speed of 6.10 m/s for 7.1 minutes. Determine the total distance which Ken ran during his 20 minute jog. A Formula One car is a single-seat racing car with an open cockpit and substantial wings located in the front and rear. At high speeds, the acrodynamics of the car help to create a strong downward force whiclh allows the car to brake from 27.8 m/s (100 km/hr or 62.2 mi/hr) to 0 in as small of a distance as 17 meters. Determine the deceleration rate (i.e., acceleration) achieved by such a car and the time that it takes.

Explanation / Answer

Motion in one dimension

Given that x(t) = 2t^4 -3t^2

a) for first two seconds

x(2) = (2*2^4) - (3*2^2) = 20 m

b) v_avg = x/t = 20/2 = 10 m/s

c) v(t) = dx/dt = 8t^3 - 6t

at t = 0

v = 0

at t = 2sec

v(2) = (8*2^3) - (6*2) = 52/2 = 26 m/s

average accelaration is a = (26-0)/2 = 13 m/s^2

d) Instantaneous velocity at t = 4 sec is

v = (8*4^3)-(6*4) = 488 m/s

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