### 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

## Show Answer

#### 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