Question

A particle moves in a straight line obeying
the v-t graph as shown in the figure. The
average velocity of the particle over the time
T is :
(A) zero
(B)
​

Answer 1

Answer:

0 is avrag evelocityof the object

Answer 2

Complete question;

A particle moves in a straight line obeying the v-t graph as shown in the figure. The average velocity of the particle over the time T is:

1) zero

2) $\frac{v_0}{2}$

3) $\frac{2v_0}{3}$

4) $\frac{3v_0}{4}$

Answer:

Option (2)$\frac{V_0}{2}$ is the correct answer.

Explanation:

Given in the question, a particle moves in a straight line obeying the v-t graph.

• The change in position or displacement (x) divided by the time intervals (t) during which the displacement happens is the definition of average velocity.

• Based on the direction of the displacement, the average velocity might either be positive or negative. Meters per second (m/s or ms-1) is the SI measure for average velocity.

So, average velocity ($V_{average}$) = $\frac{Total \ distance \ travel }{Total\ time\ taken}$

And this can be also written as,

Average velocity = $\frac{Under \ area \ of\ v- t\ graph}{Time}$

⇒$V_{avg}$ = $\frac{\frac{1}{2}(V_0 T) }{T}$ =$\frac{V_0}{2}$    [where T , T are cancel out]

Hence, the average velocity of the particle over the time is $\frac{V_0}{2}$.

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