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For the velocity-time graph as shown in the figure, in a time interval from t = 0 to t = 6 s, match the following columns and mark the correct option from the codes given below.
Column I Column II
(A) Change in velocity (p) $-$ 5/3 SI unit
(B) Average acceleration (q) $-$ 20 SI unit
(C) Total displacement (r) $-$ 10 SI unit
(D) Acceleration at t = 3 s (s) $-$ 5 SI unit
Codes
A B C D

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r p r s

p r q s

q p s r

p r s q

answer is C.

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Detailed Solution

$v_{1} = + 10 {ms}^{- 1} and v_{f} = 0$

$∴$ $Δ v = v_{f} - v_{i} = - 10 {ms}^{- 1}$

$a_{av} = \frac{Δ v}{Δ t} = \frac{- 10}{6} = \frac{- 5}{3} {ms}^{- 2}$

Total displacement = Area under v-t graph (with sign)

$= \frac{1}{2} \times 10 \times 2 - \frac{1}{2} \times 2 \times 10 - \frac{1}{2} \times 2 \times 10 = - 10 m$

and acceleration = slope of v- t graph

$= - \frac{10}{2} = - 5 {ms}^{- 2}$

Hence, $A \to r, B \to p, C \to r, D \to s$

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