A point p moves in counter -clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out the length s = t3 + 5, where s is metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2 s is nearly from Physics Motion in A Plane Class 11 Manipur Board
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A point p moves in counter -clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out the length s = t3 + 5, where s is metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2 s is nearly

  • 13 ms-2

  • 12 ms-2

  • 7.2 ms-2

  • 14 ms-2


D.

14 ms-2

Given that, s  =t3 +5
therefore speed v, = ds/st = 3t2
and rate of change of speed, at = dv/dt = 6t
∴ Tangential acceleration at t =2s
at = 6 x 2  = 12 ms-1
and at t = 2s, v = 3 (2)2 = 12 ms-1
∴ Centripetal acceleration, ac = v2/R = 144/20 ms-2
∴ Net acceleration  = square root of straight a subscript straight t superscript 2 space plus straight a subscript straight c superscript 2 end root space almost equal to space 14 space ms to the power of negative 2 end exponent

Given that, s  =t3 +5
therefore speed v, = ds/st = 3t2
and rate of change of speed, at = dv/dt = 6t
∴ Tangential acceleration at t =2s
at = 6 x 2  = 12 ms-1
and at t = 2s, v = 3 (2)2 = 12 ms-1
∴ Centripetal acceleration, ac = v2/R = 144/20 ms-2
∴ Net acceleration  = square root of straight a subscript straight t superscript 2 space plus straight a subscript straight c superscript 2 end root space almost equal to space 14 space ms to the power of negative 2 end exponent

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