Question

When a particle covers first half of the distance with a speed of 40 m/s and the next half of the distance with a speed of 80 m/s calculate average speed .

Answer 1

Answer:

The total average speed is 120 m/s

Answer 2

Answer:

• Speed for the first half of the distance = 40 m/s
• Speed for the second half of the distance = 80 m/s
• Average Speed = ?

$\displaystyle\underline{\bigstar\:\textsf{According to the given Question :}}$

• So here we shall first find the time taken by the body by assuming the two times as x/2 using the speed formula [Speed = Distance/Time]. And then simply substituting the values on the formula for average speed we shall get our Answer!!

$\displaystyle\sf :\implies t_1 = \dfrac{\dfrac{x}{2}}{v_1}$

$\displaystyle\sf :\implies t_1 = \dfrac{x}{2} \times \dfrac{1}{40}$

$\displaystyle\sf :\implies\red{t_1 = \dfrac{x}{80}}$

Similarly the time taken for d² will be,

$\displaystyle\sf :\implies t_2 = \dfrac{\dfrac{x}{2}}{v_2}$

$\displaystyle\sf :\implies t_2 = \dfrac{x}{2} \times \dfrac{1}{80}$

$\displaystyle\sf :\implies\red{t_2 = \dfrac{x}{160}}$

$\displaystyle\underline{\bigstar\:\textsf{Average Speed of the particle :}}$

$\displaystyle\sf \dashrightarrow Avg \ Speed = \dfrac{Total \ Distance}{Total \ Time}$

$\displaystyle\sf \dashrightarrow Avg \ Speed = \dfrac{\dfrac{x}{2}+\dfrac{x}{2}}{\dfrac{x}{80}+\dfrac{x}{160}}$

$\displaystyle\sf \dashrightarrow Avg \ Speed = \dfrac{\dfrac{2x}{2}}{\dfrac{2x}{160}+\dfrac{x}{160}}$

$\displaystyle\sf \dashrightarrow Avg \ Speed = \dfrac{x}{\dfrac{3x}{160}}$

$\displaystyle\sf \dashrightarrow Avg \ Speed = x\times \dfrac{160}{3x}$

$\displaystyle\sf \dashrightarrow Avg \ Speed = \dfrac{160}{3}$

$\displaystyle\sf \dashrightarrow\underline{\boxed{\sf Avg \ Speed = 53.4 \ m/s}}$

$\displaystyle\therefore\:\underline{\textsf{Average Speed of the parcel is \textbf{53.4 m/s}}}$