Question:
The distance travelled by a particle is related to time $t$ as $x=4 t^2$ The velocity of the particle at $t-5 s$ is:-
The distance travelled by a particle is related to time $t$ as $x=4 t^2$ The velocity of the particle at $t-5 s$ is:-
Updated On: Apr 28, 2025
- $8 \,m s^{-1}$
- $20\, ms ^{-1}$
- $25\, ms ^{-1}$
- $40\, ms ^{-1}$
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The Correct Option is D
Approach Solution - 1
The correct answer is (D) : $40\, ms ^{-1}$
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Approach Solution -2
The velocity \( v \) of the particle is the derivative of the position with respect to time. Given the position function:
\[
v = \frac{dx}{dt} = \frac{d}{dt}(4t^2) = 8t
\]
At \( t = 5 \) seconds, the velocity is:
\[
v = 8 \times 5 = 40 \, \text{m/s}
\]
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
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