Question

A particle moves on a straight line, and its v - t graph is shown.
List - I gives some quantites, and List - II gives some possible magnitudes of quantites, then correct match is

$\begin{array}{cc}\text{List - I}& \text{List - II}\\ \text{I) Average velocity of 4 sec}& \text{P) 0}\\ \text{II) Average acceleration of 4 sec}& \text{Q) 5}\\ \text{III) Displacement in 4 sec}& \text{R) 10}\\ \text{IV) Velocity at t = 4 sec}& \text{S) 20}\\ & \text{T) 40}\\ & \text{U) 50}\end{array}$

• A. $I\to R,II\to Q,III\to S,IV\to P$
• B. $I\to Q,II\to P,III\to S,IV\to R$
• C. $I\to Q,II\to P,III\to S,IV\to P$
• D. $I\to Q,II\to P,III\to T,IV\to P$

Answer 1

The correct option is C $I\to Q,II\to P,III\to S,IV\to P$

$<v>=\frac{\Delta x}{\Delta t}=\frac{\text{Area under v - t graph}}{\Delta t}=\frac{\frac{1}{2}\times 4\times 10}{4}=5m/s$
$<a>=\frac{v_f-v_i}{\Delta t}=\frac{0-0}{4}=0m/s^2$
Displacement = Area under graph $=\frac{1}{2}\times 4\times 10=20m$
$v_{t=4}=0$