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

Infinity Learn · Accepted Answer

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 $$acceleration=vf-vi$$△$$t=-4-128=-2$$ $$ms-2$$

Rectilinear Motion

Remember concepts with our Masterclasses.

A particle moves in positive x-direction according to law $x = 12 t - t^{2} m$ . 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 is

Average velocity is defined as
$v_{av} = \frac{Displacement}{Time Interval} = \frac{Δx}{Δt} = \frac{x_{2} - x_{1}}{t_{2} - t_{1}}$
$\Rightarrow v_{av} = \frac{[12 (8) - (8)^{2}] - 0}{8 - 0} = 4 {ms}^{- 1}$

Average speed from t=0 to t = 8 s is

Average acceleration from t= 0s to t= 8s is

Average acceleration is the rate of change of velocity.
$v = 12 - 2 t t = 0, v_{i} = 12 t = 8, v_{f} = - 4 Average acceleration = \frac{v_{f} - v_{i}}{△ t} = \frac{- 4 - 12}{8} = - 2 {ms}^{- 2}$

Ready to Test Your Skills?

free study material