Part A The automobile is originally at rest 8-0. It then starts to increase its

Question

Part A The automobile is originally at rest 8-0. It then starts to increase its speed at U = (0.05t*) ft /s2, where t is in seconds Determine the magnitude of its velocity at 8 = 465 ft. (Figure 1) Express your answer to three significant figures and include the appropriate units. | Value | Units | Submit equest Answer Figure 1of1 Part B Determine the magnitude of its acceleration at 8 = 465 ft Express your answer to three significant figures and include the appropriate units. 300 ft Value Units 240 ft Submit equest Answer

Explanation / Answer

atime = 0.05 * t^2 ---- (1)

dv/dt = 0.05 t^2

dv = 0.05 t^2 * dt

integrating we get

V = 0.05 * t^3/3 ----(2)

v = ds/dt

ds = 0.05 * t^3/3

integrating we get

s = 0.05/3 * t^4/4

so t = (12 * s/0.05)^1/4

at

s = 465 m

t = (12 * 465/0.05)^1/4 = 18.277 ft

Subsubstitute t = 18.277 in eq (2)

V = 0.05 * 18.277^3/3

Velocity of automobile is

V = 101.756 ft/s

substitute t = 18.277 in eq (1)

atime = 0.05 * 18.277^2 = 16.702 ft/s^2

But since s = 465 is greater than 300 ft, it has tangential acceleration as well

atang = v^2/radius = 101.756^2/240 = 43.142 ft/s^2

accleration of automobile is

a = sqrt(atime^2 + atang^2) = sqrt(16.702^2 + 43.142^2)

a = 46.26 ft/s^2

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