Published by:
CGP EDU Academic Team
Published on: September 12, 2026
The position of a particle moving in XY-plane varies with time 
as 
.
(i) What is the path traced by the particle?
(ii) When does the particle cross X-axis?
Text Solution
Verified by ExpertsThe correct answer is:
B
(i) Path Traced by the Particle:
The position of the particle is given by the equations:
$x = t$
$y = 3t - 5$
To eliminate time and understand the path traced in the XY-plane, we can express $y$ in terms of $x$. Since $x = t$, we can substitute into the equation for $y$:
$y = 3x - 5$
This is the equation of a straight line with a slope of 3 and a y-intercept of -5.
(ii) When does the Particle Cross the X-axis?
The particle crosses the X-axis when $y = 0$. Setting the equation for $y$ to 0, we have:
$0 = 3t - 5$
Solving for $t$, we find:
$3t = 5$
$t = rac{5}{3}$
Therefore, the particle crosses the X-axis at $t = \frac{5}{3}$.
Therefore, the correct answer for the path and the crossing point of the X-axis are B.
The position of the particle is given by the equations:
$x = t$
$y = 3t - 5$
To eliminate time and understand the path traced in the XY-plane, we can express $y$ in terms of $x$. Since $x = t$, we can substitute into the equation for $y$:
$y = 3x - 5$
This is the equation of a straight line with a slope of 3 and a y-intercept of -5.
(ii) When does the Particle Cross the X-axis?
The particle crosses the X-axis when $y = 0$. Setting the equation for $y$ to 0, we have:
$0 = 3t - 5$
Solving for $t$, we find:
$3t = 5$
$t = rac{5}{3}$
Therefore, the particle crosses the X-axis at $t = \frac{5}{3}$.
Therefore, the correct answer for the path and the crossing point of the X-axis are B.
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