(7%) Problem 6: in seconds and x is in meters. The x-coordinate of an object var

Question

(7%) Problem 6: in seconds and x is in meters. The x-coordinate of an object varies with time according to the following expression: r ) 3 + 5, + 9r2. where t s 25% Part (a) Write an expression for the x-component of the velocity as a function of time. Grade Sun Submissios Attempts ru 10% per al detailed vi 1 2 3 SubmitHint Feedback: 0% deduction per feedback. Hints: 5% deduction per hint. Hints remaining:- 25% Part (b) write an expression for the x-component of the acceleration as a function of time. rt (c) Find the x-component of the average velocity, in meters per second, between 0.18 s and 1-0.93 Find the x-component of acceleration, in meters per second sq uared, at ,2-093 s. 25% Part (d)

Explanation / Answer

here,

x = 3 + 5 t + 9 t^2 .......(1)

a)

differentiating equation(1) for velocity

v = dx/dt = 5 + 18 * t ....(2)

b)

differentiating the equation for accelration

a = dv/dt = 18 m/s^2

c)

at t1 = 0.18 s

x1 = 3+ 5 * 0.18 + 9 * 0.18^2 m

x1 = 4.1916 m

at t2 = 0.93 s

x2 = 3 + 5 * 0.93 + 9 * 0.93^2 m

x2 = 15.4 m

the average velocity , v = (x2 - x1)/(t2 - t1)

v = ( 15.4 - 4.1916) /(0.93 - 0.18) m/s

v = 14.9 m/s

d)

the accelration is constant i.e 18 m/s^2

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