Question

Position-time (x-t ) graph of a particle moving along x-axis is as shown in the figure.The average speed of particle in time interval t=0 to t=10 s is?

• A. $20m{s}^{-1}$
• B. $\frac{4}{5}m{s}^{-1}$
• C. $1m{s}^{-1}$
• D. $\frac{5}{4}m{s}^{-1}$

Answer 1

Answer: (C)

Step 1: Given

Time between 2-0 sec(T₁)= 2 sec

Total time(T)= 10 sec

Time between 10-8 sec(T₃)= 2 sec

Distance covered between 0-2 sec(D₁)= 10 m

Distance covered between 2-8 sec(D₂)= 0 m

Distance covered between 8-10 sec(D₃)= 10 m

Step 2: Formula used

velocity= $\frac{Distance}{time}$

Step 3: Finding the average velocity

Velocity(v₁)=$\frac{\text{D₁}}{T₁}$ =$\frac{10}{2}$ = 5 m/s

Velocity(v₃)=$\frac{D_3}{T_3}$ = $\frac{10}{2}$ = 5 m/s

Since, the particle has zero velocity in between.

Average velocity= $\frac{v_1+v_3}{totaltime\left(T\right)}$

Average velocity= $\frac{5+5}{10}$= $\frac{10}{10}$ m/s

Average velocity=1 m/s

Hence, option C(1 m/s) is correct.