Question:
Two particles A and B are moving along positive x- and positive y-axes respectively with the same speed v m s$^{-1}$. At t = 0, they both pass through the origin. The equation of the straight line joining A and B at time t is:
Two particles A and B are moving along positive x- and positive y-axes respectively with the same speed v m s$^{-1}$. At t = 0, they both pass through the origin. The equation of the straight line joining A and B at time t is:
Show Hint
When two particles move along perpendicular axes with equal speed, their positions form a straight line with slope -1.
Updated On: Jul 18, 2026
- \(y(t) = x(t) + vt\)
- \(y(t) = -x(t) + vt\)
- \(y(t) = x(t)\)
- \(y(t) = -x(t)\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding motion of particle A.
Particle A moves along positive x-axis with speed \(v\), so: \[ x_A = vt, \quad y_A = 0 \]
Step 2: Understanding motion of particle B.
Particle B moves along positive y-axis with speed \(v\), so: \[ x_B = 0, \quad y_B = vt \]
Step 3: Coordinates of both particles at time t.
So at time \(t\): \[ A(vt, 0), \quad B(0, vt) \]
Step 4: Equation of line joining two points.
Slope of AB: \[ m = \frac{vt - 0}{0 - vt} = -1 \] Using point A: \[ y - 0 = -1(x - vt) \]
Step 5: Simplification.
\[ y = -x + vt \]
Step 6: Final conclusion.
Hence, equation of line is: \[ \boxed{y = -x + vt} \]
Particle A moves along positive x-axis with speed \(v\), so: \[ x_A = vt, \quad y_A = 0 \]
Step 2: Understanding motion of particle B.
Particle B moves along positive y-axis with speed \(v\), so: \[ x_B = 0, \quad y_B = vt \]
Step 3: Coordinates of both particles at time t.
So at time \(t\): \[ A(vt, 0), \quad B(0, vt) \]
Step 4: Equation of line joining two points.
Slope of AB: \[ m = \frac{vt - 0}{0 - vt} = -1 \] Using point A: \[ y - 0 = -1(x - vt) \]
Step 5: Simplification.
\[ y = -x + vt \]
Step 6: Final conclusion.
Hence, equation of line is: \[ \boxed{y = -x + vt} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Kinematics Questions
A person climbs up a conveyor belt with a constant acceleration. The speed of the belt is \( \sqrt{\frac{g h}{6}} \) and the coefficient of friction is \( \frac{5}{3\sqrt{3}} \). The time taken by the person to reach from A to B with maximum possible acceleration is:
- A body starting from rest with an acceleration of \( \frac{5}{4} \, \text{ms}^{-2} \). The distance travelled by the body in the third second is:
- When the temperature of a gas is raised from 27°C to 90°C, the increase in the rms velocity of the gas molecules is:
- The distance $s$ (in m) travelled by a particle is given by the expression $s = 5t^2 + 8t$, where $t$ is time in seconds. The acceleration of the particle is
- The velocity (v) of a particle starting from rest increases linearly with time (t) as $ v = 4t $, where v is in $ ms^{-1} $ and t is in second. The distance covered by the particle in the first 4 seconds is
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions