When a stone thrown directly upwards reaches the top, it: A. Velocity and acceleration are zero. B. The velocity is zero and the acceleration is about 10 m/s 2. C. Velocity is about 10 m/s and acceleration is zero. D. The velocity is about 10 m/s and the acceleration remains the same.
B
Understanding Motion at the Peak of a Stone's Trajectory
When a stone is thrown directly upwards, it moves against the force of gravity. Gravity causes a constant downward acceleration. As the stone rises, its upward velocity decreases due to this downward acceleration. Eventually, it reaches its highest point before starting to fall back down.
Velocity at the Highest Point
At the very peak of its trajectory, the stone momentarily stops changing direction. It is no longer moving upwards and has not yet started moving downwards. This brief moment of rest means its instantaneous velocity is zero.
Acceleration at the Highest Point
Acceleration is the rate of change of velocity. While the stone's velocity is momentarily zero at the peak, the force of gravity is still acting on it. Gravity exerts a constant downward pull, resulting in a constant downward acceleration, known as the acceleration due to gravity. This acceleration (g) is approximately $9.8 \, \text{m/s}^2$ on Earth, often rounded to $10 \, \text{m/s}^2$ for simplicity in many problems. The acceleration due to gravity does not disappear or become zero just because the object's velocity is momentarily zero.
Analyzing the Options
Let's evaluate each option based on our understanding of motion under gravity:
- Option A: Velocity and acceleration are zero.
This is incorrect. While the velocity is zero at the peak, the acceleration due to gravity is definitely not zero; it is still acting downwards.
- Option B: The velocity is zero and the acceleration is about 10 m/s².
This is consistent with our physics understanding. The velocity is momentarily zero at the highest point, and the acceleration due to gravity is approximately $10 \, \text{m/s}^2$ (downwards, though the option only gives magnitude).
- Option C: Velocity is about 10 m/s and acceleration is zero.
This is incorrect. The velocity at the peak is zero, not $10 \, \text{m/s}$. The acceleration at the peak is about $10 \, \text{m/s}^2$, not zero.
- Option D: The velocity is about 10 m/s and the acceleration remains the same.
This is incorrect regarding velocity; the velocity is zero at the peak. The statement about acceleration remaining the same is true in magnitude (it's always about $10 \, \text{m/s}^2$), but the velocity claim makes the option incorrect.
Based on the analysis, Option B accurately describes the velocity and acceleration of a stone thrown directly upwards when it reaches the top.
| Point in Trajectory | Velocity | Acceleration |
|---|---|---|
| Going Up | Decreasing (upwards) | Constant ($\approx 10 \, \text{m/s}^2$ downwards) |
| At the Top (Peak) | Zero (instantaneously) | Constant ($\approx 10 \, \text{m/s}^2$ downwards) |
| Coming Down | Increasing (downwards) | Constant ($\approx 10 \, \text{m/s}^2$ downwards) |
Revision Table: Stone Motion Concepts
| Concept | Explanation | At the Peak |
|---|---|---|
| Velocity | Speed and direction of motion | Zero (momentarily) |
| Acceleration | Rate of change of velocity | Due to gravity ($\approx 10 \, \text{m/s}^2$ downwards) |
| Force of Gravity | Pull towards the Earth | Always acting downwards |
Additional Information: Understanding Projectile Motion
A stone thrown directly upwards is a classic example of one-dimensional projectile motion under constant acceleration (due to gravity). Here are a few key points:
- The acceleration due to gravity ($g$) is approximately $9.8 \, \text{m/s}^2$ near the Earth's surface. It acts downwards regardless of the object's motion.
- The equations of motion (kinematics equations) can be used to describe the position, velocity, and time of the stone at any point in its flight, assuming air resistance is negligible.
- The time taken to reach the peak is equal to the time taken to fall back from the peak to the initial height.
- The initial upward velocity determines the maximum height reached.
It's a common misconception that acceleration is zero when velocity is zero. This is only true if the net force on the object is zero at that moment. For a stone in free flight, the force of gravity is always present, resulting in constant acceleration.
Important Questions from Relative Velocity
Rain is falling vertically on the ground at speed 5√3 m/s. If a man walks towards the East with speed 5 m/s, he will feel the rain falling at what angle to the vertical ?
When two bodies move uniformly towards each other, the distance decrease by 6 m/s. If both the bodies moves (as above) in the same direction with the same speed, the distance between them increases by 4 m/s. Then the speed of the two bodies are :
On a rainy day, rain drops fall vertically with speed \(v\). An observer is moving towards east with speed \(v\), while another observer moves towards north with the same speed \(v\). What is the angle between apparent rain directions observed by them?
