Kinematics

Concept: Motion is symmetric under constant acceleration.

Step 1: Time of ascent.


Step 2: Time of descent.
From top to ground:

The displacement is given by: To find the time at which the velocity is zero, we first find the velocity by differentiating the displacement with respect to time: Now, set to find when the velocity becomes zero: Solving for :
Thus, the time at which the velocity becomes zero is .

The displacement of a body moving with an initial velocity and constant acceleration is given by the equation: We need to find the ratio of the distances travelled by the body in the first and second 5-second intervals. - In the first interval (0 to 5 seconds), the displacement is: - In the second interval (5 to 10 seconds), the displacement is: The ratio of distances travelled in the first and second intervals is .

Particle A moves with constant velocity: Particle B starts from rest with acceleration : B overtakes A when: So, Ignoring , we get:
Hence, the correct answer is:

Step 1: Use the equation for distance under constant acceleration.
The distance covered by a body under constant acceleration is given by the equation: where:
- is the initial velocity (0 m/s, since the body starts from rest),
- is the acceleration,
- is the time.
Since the body starts from rest, the equation simplifies to:
Step 2: Calculate the distance covered in 6 seconds and 5 seconds.
We are given that the acceleration . The distance covered in 6 seconds is: The distance covered in 5 seconds is:
Step 3: Find the distance covered between 5 s and 6 s.
The distance covered between 5 s and 6 s is the difference between and : Thus, the distance covered by the body between 5 s and 6 s is:

Step 1: Understanding the Concept:
In classical kinematics, the instantaneous velocity of a moving body is defined precisely as the time derivative of its position or displacement vector.
To find the exact time when the body briefly comes to rest, we must calculate the velocity function and explicitly set it equal to zero.
Step 2: Key Formula or Approach:
The instantaneous velocity is derived from the displacement using basic differential calculus: .
Once the generalized expression for is obtained, solve the algebraic equation for time .
Step 3: Detailed Explanation:
The given displacement function with respect to time is:
Differentiate this entire equation with respect to to find the instantaneous velocity :
Applying basic power rule differentiation:
To precisely find when the velocity becomes absolute zero, we set :
Rearranging the simple linear equation:
Step 4: Final Answer:
The velocity of the moving body drops to zero exactly after .