Question

	Column I		Column II
I.	The practical A is	a.	accelerating
II.	The particle B is	b.	decelerating
III.	The particle C is	c.	speeding up
IV.	The particle D is	d.	slowing down

Figure shows the position-time graph of particle moving along a straight line. Match the entries of Column I with the entries of Column II.

Answer 1

(i) For particle A :-

(1) $\frac{dx}{dt}>0\Rightarrow v>0$

(2) As the graph of particle A is

concave downward ($\because$ slope decreases),

So, $\frac{d^{2}x}{d{t}^2}<0\Rightarrow a<0$

As velocity and acceleration is in

opposite direction, The particle A is

decelerating and slowing down

(ii) For particle B :-

(1) $\frac{dx}{dt}<0\Rightarrow v<0$

(2) As the graph of particle B is concaue

downward, so, $\frac{d^{2}x}{dt2}<0\Rightarrow a<0$

As velocity and acceleration are in same

direction, the particle B is accelerating and

speeding up

(iii) For particle C :-

(1) $\frac{dx}{dt}>\Rightarrow v>0$

(2) As the graph of particle c is concave

upward, so, $\frac{d^{2}x}{d{t}^2}>0\Rightarrow a>0$

As velocity and acceleration are in same direction,

the particle c is accelerating and speeding up.

(iv) For particle D :-

(1) $\frac{dx}{dt}<0\Rightarrow v<0$

(2) As the graph of particle D is

concave upward, $\frac{d^{2}x}{d{t}^2}>0\Rightarrow a>0$

As velocity and acceleration are in opposite direction,

the particle D is decelerating and slowing down