Question

The average velocity of Ram over a given time duration is $12\text{m/s}$. If he travels the first half of the total time with velocity $x\text{m/s}$ and the seconds half of the total time with velocity $2x\text{m/s}$. Calculate the value of $x$.

• A. $10\text{m/s}$
• B. $4\text{m/s}$
• C. $8\text{m/s}$
• D. $2\text{m/s}$

Answer 1

The correct option is C $8\text{m/s}$


Let the total time be $2t$
Distance travelled by Ram in going from $A$ to $C$
$d_1=x\times t=xt$
Distance travelled by Ram in going from $C$ to $B$
$d_2=2x\times t=2xt$
Total distance $=d_1+d_2=(x+2x)t=3xt$
Average speed $=3x=24$
$x=8\text{m/s}$

Alternative method:
As, the velocity of Ram is changing at uniform rate x = 8 m/s