Question:
At time t = 0 a particle starts travelling from a height \(7\hat z cm\) in a plane keeping \(z\) coordinate constant. At any instant time it's position along the \(x\) and \(y\) directions are defined as \(3t\) and \(5t^3\) respectively. At \(t = 1s\) acceleration of the particle will be
At time t = 0 a particle starts travelling from a height \(7\hat z cm\) in a plane keeping \(z\) coordinate constant. At any instant time it's position along the \(x\) and \(y\) directions are defined as \(3t\) and \(5t^3\) respectively. At \(t = 1s\) acceleration of the particle will be
Updated On: Jul 8, 2024
- \(-30 \hat {y}\)
- \(30\hat {y}\)
- \(3 \hat {x}+ 15\hat {y}\)
- \(3\hat{x}^+15\hat{y}+7\hat{z}\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
\(\vec r=3t\hat {i}+5t^3\hat{j}+7\hat{k}\)
\(\frac{d^2\vec r}{dt^2}=30t\hat{j}\) At \(t=1\)
⇒ \(\frac{d^2\vec r}{dt^2}\)= \(30\hat{j}\)
Was this answer helpful?
0
0
Top Questions on Motion in a plane
- A person travelling on a straight line moves with a uniform velocity \( v_1 \) for a distance \( x \) and with a uniform velocity \( v_2 \) for the next \( \frac{3x}{2} \) distance. The average velocity in this motion is \( \frac{50}{7} \, \text{m/s} \). If \( v_1 \) is 5 m/s, then \( v_2 \) is ___ m/s.
- JEE Main - 2025
- Physics
- Motion in a plane
- A ball is thrown vertically upwards with an initial velocity of $ 20 \, \text{m/s} $. How high will the ball rise? (Take $ g = 10 \, \text{m/s}^2 $)
- MHT CET - 2025
- Physics
- Motion in a plane
- The minimum velocity of a projectile is 50% of its maximum velocity. If the minimum velocity of the projectile is $10~\text{m s}^{-1}$ then the time of flight of the projectile is (Acceleration due to gravity = $10~\text{m s}^{-2}$
- TS EAMCET - 2025
- Physics
- Motion in a plane
- A cannon on a cliff 55 m above the ground fires a shell with a velocity of \(50\hat{i}+50\hat{j}\) ms\textsuperscript{−1}. The displacement vector of the shell when it hits the ground is (Acceleration due to gravity = 10 ms\textsuperscript{−2})
- TS EAMCET - 2025
- Physics
- Motion in a plane
- If a body projected with a velocity of 19.6 ms⁻¹ reaches a maximum height of 9.8 m, then the range of the projectile is (Neglect air resistance)
- TS EAMCET - 2025
- Physics
- Motion in a plane
View More Questions
Questions Asked in JEE Main exam
Match the LIST-I with LIST-II for an isothermal process of an ideal gas system.
Choose the correct answer from the options given below:
- JEE Main - 2026
- Thermodynamics and Work Done
- A bag contains 10 balls out of which \( k \) are red and \( (10-k) \) are black, where \( 0 \le k \le 10 \). If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:
- JEE Main - 2026
- Probability
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?
- JEE Main - 2026
- Organic Chemistry
- For two identical cells each having emf \(E\) and internal resistance \(r\), the current through an external resistor of \(6\,\Omega\) is the same when the cells are connected in series as well as in parallel. The value of the internal resistance \(r\) is ________ \(\Omega\).
- JEE Main - 2026
- Current electricity
- For three unit vectors \( \vec a, \vec b, \vec c \) satisfying \[ |\vec a-\vec b|^2 + |\vec b-\vec c|^2 + |\vec c-\vec a|^2 = 9 \] and \[ |2\vec a + k\vec b + k\vec c| = 3, \] the positive value of \( k \) is:
- JEE Main - 2026
- Vector Algebra
View More Questions
Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration