I need the work shown. Answers are: 3. t = 10.3 sec, v = 61.8 ft/sec 4. v = 3u_r

Question

I need the work shown. Answers are:
3. t = 10.3 sec, v = 61.8 ft/sec 4. v = 3u_r + 4u_th, a = -23/3u_r + 20 u_th 3. A car starts from rest at A and increases its speed around a circular track at 6 ft/sec. Determine the (a) time and (b) speed at which the car's acceleration magnitude reaches 20 ft/sec?. The track has a radius of 200 ft. 200 ft 4. A pin P is moving outward along the slot of the horizontal circular disk. Its radial coordinate is given by r = 3 t2 / 2 meters. The disk turns such that = 4 t2 / 3 radians. Find the (a) velocity and (b) acceleration of P at 1 s. Express the answers as vectors of radial and circumferential components.

Explanation / Answer

3) considering after time t

So tangential speed at that time (v) = 6t

Centripetal acceleration (ac) = v²/r = 36t²/200 = 0.18t²

So net acceleration = sqrt(ac² +at²) = sqrt(0.0324t + 36)

20² = 0.0324t +36

0.0324t = 400-36 = 364

t = 364/0.0324 = 11234.568

t = 10.295 = 10.3 s

So speed at that time = 10.3×6 = 61.8 ft/s

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