Published by:
CGP EDU Academic Team
Published on: September 12, 2026
If velocity of a particle is given by 
, then find average velocity in interval 
.
Text Solution
Verified by ExpertsThe correct answer is:
A
To find the average velocity over the interval \(0 \leq t \leq 1\), we use the formula for average velocity:
Average Velocity = \( \frac{1}{b-a} \int_{a}^{b} v(t) \, dt \)
Here, \(a = 0\) and \(b = 1\).
The velocity function is given as \(v(t) = 2t + 3\).
First, we integrate \(v(t)\):
\(\int_{0}^{1} (2t + 3) \, dt = [t^2 + 3t]_{0}^{1} = (1^2 + 3(1)) - (0^2 + 3(0)) = 1 + 3 = 4\)
Now applying the average velocity formula:
Average Velocity = \( \frac{1}{1-0} (4) = 4 \, m/s\)
Therefore, the answer is 4 m/s.
Average Velocity = \( \frac{1}{b-a} \int_{a}^{b} v(t) \, dt \)
Here, \(a = 0\) and \(b = 1\).
The velocity function is given as \(v(t) = 2t + 3\).
First, we integrate \(v(t)\):
\(\int_{0}^{1} (2t + 3) \, dt = [t^2 + 3t]_{0}^{1} = (1^2 + 3(1)) - (0^2 + 3(0)) = 1 + 3 = 4\)
Now applying the average velocity formula:
Average Velocity = \( \frac{1}{1-0} (4) = 4 \, m/s\)
Therefore, the answer is 4 m/s.
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