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:-

Updated On: Mar 19, 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:

  1. Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
  2. Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.