Question

Consider a 2.0-kgkg object that moves along the x axis according to the expression x(t)=ct3x(t)=ct3, where cc = +0.230 m/s3m/s3 .

Determine the xx component of the object's average velocity during the interval from titi = 0.500 ss to tftf = 1.50 ss. Use all significant digits provided by your calculator?

Repeat for the interval from titi = 0.950 ss to tftf = 1.05 ss. Use all significant digits provided by your calculator?

Repeat for the interval from titi = 0.995 ss to tftf = 1.005 ss. Use all significant digits provided by your calculator?

Determine the xx component of the object's velocity at tt = 1.00 ss ?

Answer 1

given
m = 2.0 kg
x(t) = c*t^3

= 0.23*t^3

a) ti = 0.5 s and tf = 1.5 s
at ti = 0.5 s, xi = 0.23*0.5^3 = 0.02875 m
at tf = 1.5 s, xf = 0.23*1.5^3 = 0.77625 m

acerage velocity, v_avg = (xf - xi)/(tf - ti)
= (0.77625 - 0.02875)/(1.5 - 0.5)
= 0.7475 m/s <<<<<<<------------------Answer

b) ti = 0.95 s and tf = 1.05 s
at ti = 0.95 s, xi = 0.23*0.95^3 = 0.197196 m
at tf = 1.05 s, xf = 0.23*1.05^3 = 0.266254 m

acerage velocity, v_avg = (xf - xi)/(tf - ti)
= (0.266254 - 0.197196)/(1.05 - 0.95)
= 0.691 m/s <<<<<<<------------------Answer

c) ti = 0.995 s and tf = 1.005 s
at ti = 0.995 s, xi = 0.23*0.995^3 = 0.226567 m
at tf = 1.005 s, xf = 0.23*1.005^3 = 0.233467 m

acerage velocity, v_avg = (xf - xi)/(tf - ti)
= (0.233467 - 0.226567)/(1.005 - 0.995)
= 0.690 m/s <<<<<<<------------------Answer

d) instantaneous velocity, v = dx/dt

= 0.23*3*t^2

= 0.69*t^2

at t = 1 s

v = 0.69*1^2

= 0.69 m/s <<<<<<<------------------Answer