In projectile motion, the modulus of rate of change of speed

Options

A. is constant
B. first increases then decreases
C. first decreases then increases
D. none of the above

Answer

To solve the question regarding the modulus of the rate of change of speed in projectile motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Projectile Motion**:
- Projectile motion involves an object moving in a curved path under the influence of gravity. The motion can be analyzed in two dimensions: horizontal and vertical.

2. **Define Speed and Velocity**:
- Speed is the magnitude of velocity. Velocity is a vector quantity that has both magnitude and direction. The rate of change of speed refers to how quickly the speed of the object is changing.

3. **Identify Forces Acting on the Projectile**:
- In projectile motion, the only force acting on the object after it is projected is gravity, which acts downwards.

4. **Rate of Change of Velocity**:
- The rate of change of velocity is influenced by acceleration. In the case of projectile motion, the vertical component of velocity changes due to gravitational acceleration (g), which is approximately 9.81 m/s² downward.

5. **Modulus of Rate of Change of Speed**:
- The modulus of the rate of change of speed refers to the absolute value of the change in speed over time. Since the acceleration due to gravity is constant, the rate of change of speed (which is the same as the rate of change of velocity in the vertical direction) is also constant.

6. **Conclusion**:
- Since the gravitational acceleration is constant throughout the projectile's flight, the modulus of the rate of change of speed is also constant. Therefore, the correct answer is option 1: constant.

### Final Answer:
The modulus of the rate of change of speed in projectile motion is constant.

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