Question:

Initial velocity of a particle is $u$ at time $t = 0$. If acceleration $f $ of the particle is given by at, then the valid relation is

Updated On: Jul 6, 2022
  • $\upsilon=u+at$
  • $\upsilon=u+\frac{1}{2}at^2$
  • $\upsilon=u+at^2$
  • $\upsilon=u$
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The Correct Option is B

Solution and Explanation

$f = \frac{d \upsilon}{dt} = at$ i.e. $d \, \upsilon = at \, dt $ $\int\limits^{\upsilon}_{\upsilon} d \, \upsilon = \int\limits^t_0 \, at \, dt$ i.e. $\upsilon - u = \frac{1}{2} at^2$ i.e. $\upsilon =u + \frac{1}{2} at^2$
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Notes on Motion in a straight line

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.