course phy 201
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A ball starting from rest rolls 11 cm down an incline on which its acceleration is 27 cm/s2, then onto a second incline 44 cm long on which its acceleration is 9 cm/s2. How much time does it spend on each incline?s = v0t + .5at^2 The initial velocity is 0cm/s so t = srt(2*s/a) = 0.9s for the fir
Now we need to find the final velocity for this ramp which will be the initial velocity for the other ramp. vAve = ‘ds/’dt = 11cm/.9s = 12.2cm/s
vAve = (v0 + vf)/2 sp vf = 2 * vAve – v0 = 2 * 12.2cm/s – 0cm/s = 24.4 cm/s
Now initial velocity of second is 24.4cm/s
To find final velocity take equation v^2 = v0^2 + 2a(s)
vf = srt( v0^2 +2a(s)) = srt( 24.4cm/s +2 * 9cm/s^2 * 44cm = 37.2cm/s
a = ‘dv/’dt = ‘dt = ‘dv/a = (37.2cm/s – 24.4cm/s) / 9cm/s^2 = 1.4s
Good work. Let me know if you have questions.