A particle moving in a straight line covers half the distance wit… - Vidyadip

MCQ

A particle moving in a straight line covers half the distance with speed of $3 \,m/s$. The other half of the distance is covered in two equal time intervals with speed of $4.5 \,m/s$ and $7.5 \,m/s$ respectively. The average speed of the particle during this motion is...... $\,m/s$

✓
$4$
B
$5$
C
$5.5 $
D
$4.8$

✓

Answer

Correct option: A.

$4$

a
(a) If ${t_1}$ and $2{t_2}$ are the time taken by particle to cover first and second half distance respectively.

${t_1} = \frac{{x/2}}{3} = \frac{x}{6}$…(i)

${x_1} = 4.5\;{t_2}$ and ${x_2} = 7.5\;{t_2}$

So, ${x_1} + {x_2} = \frac{x}{2} \Rightarrow 4.5{t_2} + 7.5{t_2} = \frac{x}{2}$

${t_2} = \frac{x}{{24}}$…(ii)

Total time $t = {t_1} + 2{t_2} = \frac{x}{6} + \frac{x}{{12}} = \frac{x}{4}$

So, average speed $ = 4\;m/sec$.

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