एखादी वस्तू x = 0 m पासून विश्रांतीपासून सुरू होते आणि x-अक्षाच्या बाजूने 1.6 m/s2 च्या स्थिर प्रवेगसह हलते. x = 12.8 m ते x = 20.0 m या प्रवासादरम्यान, त्याचा सरासरी वेग __________ असेल.

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  1. 7.2 m/s
  2. 3.6 m/s
  3. 8.8 m/s
  4. 2.4 m/s

Answer (Detailed Solution Below)

Option 1 : 7.2 m/s
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संकल्पना:

गतीचे समीकरण:

  • किनेमॅटिक्सच्या गतीची समीकरणे वस्तूच्या गतीच्या मूलभूत संकल्पनेचे वर्णन करतात जसे की एखाद्या वस्तूची स्थिती, वेग किंवा वेगवेगळ्या वेळी प्रवेग.
  • गतीची ही तीन समीकरणे 1D, 2D आणि 3D मधील वस्तूची गती नियंत्रित करतात.
  • तीन समीकरणे: v = u + at, s = ut + 0.5 at2, 2as = v2 - u2
  • येथे, u = प्रारंभिक वेग, v = अंतिम वेग, s = विस्थापन, t = वेळ
  • गुरुत्वाकर्षणाच्या प्रभावाखाली, त्वरण a ची जागा गुरुत्वाकर्षणामुळे प्रवेगने घेतली जाते.

गणना:

Given,

Initial velocity, u = 0 m/s, Acceleration, a = 1.6 m/s2

From the second equation of motion,

s = ut +0.5 at2

12.8 = 0.8 t12

\(t^2=\frac{12.8}{0.8}=16\)

t1 = 4 sec.

For s = 20

12.8 = 0 × t2 + 0.5 × 1.6 t22

t2 = 5 sec.

The average velocity can be calculated as,

\(v_{avg}=\frac{total\, \, displacement}{total\, \, time\, duration}\)

\(v_{avg}=\frac{20 - 12.8}{5 - 4}=7.2m/s\)

Hence, What is its average velocity 7.2m/s.

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