Question

A particle is moving in a straight line according to the formula \[s = {t^2} + 8t + 12\]. If s be measured in meter and t be measured in second then find the average velocity of the particle in the third second.
A.14 m/sec
B. 13 m/sec
C. 15 m/sec
D. none of these

Answer 1

Hint: First substitute 3 for $t$ in the expression of $s$ then substitute 2 in that expression, after that subtract \[s(2)\] from \[s(3)\] to obtain the required solution.

Complete step by step solution:
The average velocity in the third second is equal to the distance traveled in the third second.
 Hence we have to calculate \[s(3) - s(2)\] to obtain the required answer.
The given expression is \[s = {t^2} + 8t + 12\].
Substitute 3 for t in the given quadratic equation to obtain the value of \[s(3)\].
\[s(3) = {3^2} + 8 \times 3 + 12\\
\Rightarrow s(3) = 9 + 24 + 12\\
\Rightarrow s(3) = 45\]
Substitute 2 for t in the given quadratic equation to obtain the value of \[s(2)\].
\[s(2) = {2^2} + 8 \times 2 + 12\\
\Rightarrow s(2) = 9 + 24 + 12\\
\Rightarrow s(2) = 32\]
Subtract 32 from 45 to obtain the average velocity.
\[45 - 32 = 13\]

Therefore the correct option is B.

Note: Students often substitute 3 for t in the given equation of \[s = {t^2} + 8t + 12\] and wrote the answer as 45 but we are asked to find the average velocity so first we need to substitute 3 for t then 2 for t and need to subtract \[s(2)\] from \[s(3)\] to obtain the required answer 13.