A particle moves in positive $$x-direction$$ according to law $$x=12t$$−$$t2m$$. where t time in second. (Take$$ $$+ve$$ $$x-axis$$ as $$+ve).Based on the above facts, answer the following questions.Average velocity from $$t=0$$ to $$t=8$$ s isAverage speed from $$t=0$$ to t $$=$$ $$8$$ s isAverage acceleration from $$t=$$ $$0s$$ to $$t=$$ $$8s$$ is

Question

A particle moves in positive $$x-direction$$ according to law $$x=12t$$−$$t2m$$. where t time in second. (Take$$ $$+ve$$ $$x-axis$$ as $$+ve).Based on the above facts, answer the following questions.Average velocity from $$t=0$$ to $$t=8$$ s isAverage speed from $$t=0$$ to t $$=$$ $$8$$ s isAverage acceleration from $$t=$$ $$0s$$ to $$t=$$ $$8s$$ is

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Average velocity is defined $$asvav=$$ Displacement  Time Interval $$=$$ΔxΔ$$t=x2$$−$$x1t2$$−$$t1$$⇒ $$vav=12(8)$$−$$(8)2$$−$$08$$−$$0=4ms$$−$$1To$$ calculate the average speed, we must first find the instant of reversal of motion, i.e. when v $$=$$ $$0$$. $$Sincev=dxdt=12$$−$$2t$$⇒    $$v=0$$⇒    $$t=6sSo$$ distance travelled by the particle from t $$=$$ $$0$$ to t $$=$$ $$8s$$ $$isl=$$|$$36$$−$$0$$|$$+$$|$$32$$−$$36$$|$$=40mSo$$ average speed is Average Speed $$=$$ Total Distance Travelled  Total Time Taken ⇒  Average Speed $$=408=5ms$$−$$1Average$$ acceleration is the rate of change of velocity.$$v=12-2t$$ $$t=0$$, $$vi=12$$ $$t=8$$, $$vf=-4$$ Average $$acceleration=vf-vi$$△$$t=-4-128=-2$$ $$ms-2$$

A particle moves in positive x-direction according to law x=12t−t2m. where t time in second. (Take +ve x-axis as +ve).Based on the above facts, answer the following questions.Average velocity from t=0 to t=8 s isAverage speed from t=0 to t = 8 s isAverage acceleration from t= 0s to t= 8s is

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