The following plots show variation of velocity (v$v$) with time (t$t$), of a ball thrown vertically upward, and falling back. Which of the following plots is/are correct? A.

B.

C.

D.

E.

Related Formula

Since initial velocity u = 0$u = 0$, S = (1)/(2)gt²$S = \frac{1}{2}gt^2$

Core Logic

The distance travelled by the free-falling ruler before being caught depends purely on the reaction time (t$t$) of the person. Since S ∝ t²$S \propto t^2$, a longer reaction time results in a greater distance travelled by the ruler.

Step 1: Order Calculation

Sort the given reaction times in descending order: tB = 0.22 ~s$t_B = 0.22 \mathrm{~s}$ tE = 0.21 ~s$t_E = 0.21 \mathrm{~s}$ tA = 0.20 ~s$t_A = 0.20 \mathrm{~s}$ tD = 0.19 ~s$t_D = 0.19 \mathrm{~s}$ tC = 0.18 ~s$t_C = 0.18 \mathrm{~s}$

Thus, tB > tE > tA > tD > tC$t_B > t_E > t_A > t_D > t_C$. Consequently, the distance order is exactly identical: SB > SE > SA > SD > SC$S_B > S_E > S_A > S_D > S_C$.

Pattern Recognition

Distance in free fall always scales monotonically with time. The sequence of distances purely mirrors the numeric ranking of the given reaction times without calculating any actual distances.

Chapter Mix

Class 11 Physics: Motion in a Straight Line