Motion In One Dimension Question 6
Question 6 - 30 January - Shift 1
A horse rider covers half the distance with $5 m / s$ speed. The remaining part of the distance was travelled with speed $10 m / s$ for half the time and with speed $15 m / s$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $x / 7 m / s$. The value of $x$ is
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Answer: (50)
Solution:
Formula: Average velocity
$t _{AB}=\frac{x}{5 m / s}$
In motion $BC$
$x=d_1+d_2$
where $d_1 \& d_2$ we the distance travelled with 10
$m / s$ and $15 m / s$ respectively in equal time intervals
$\frac{’ t}{2}$ each
$d_1=\frac{10 t}{2}, d_2=\frac{15 t}{2}$
$d_1+d_2=x=\frac{t}{2}(10+15)=\frac{25 t}{2}$
$\langle v\rangle=\frac{2 x}{\frac{x}{5}+\frac{2 x}{25}}=\frac{2 \times 25}{5+2}=\frac{50}{7} m / s$
Ans. : 50
