Question

A particle has a rectilinear motion and the figure gives its displacement as a function of time. Which of the following statements is false with respect to the motion?

• A. Between O and A the velocity is positive and acceleration is negative
• B. Between A and B the velocity and acceleration are positive
• C. Between B and C the velocity is negative and acceleration is positive
• D. Between C and D the acceleration is positive.

Answer 1

The correct option is B Between A and B the velocity and acceleration are positive

the slope of $x-t$ graph gives velocity

Slope is divided by $\tan \theta$

$\theta =$ angle from $+ve$ horizontal axis

(time axis in our case)

double derivative of $r-t$ graph will give

slope of slope acceleration

as $0=\frac{d^{2}x}{a{t}^2}$

$0$ to $A$ all tangent have $+ve$ slope so velocity $+ve$

going $0$ to $A$ the alope tangent is

decreases $\Rightarrow$ velocity decreases

So acceleration is $-ve$

checking similarly

$B$ is formed to be wrong (False)

as tangent between $A$ and $B$ are having $-ve$ slope do $-ve$ velocity