A car moves on a circular road. It describes equal angles about the centre in equal intervals of time. Which of the following statement about the velocity of the car is true

Options

A. Velocity is constant
B. Magnitude of velocity is constant but the direction changes.
C. Both magnitude and direction of velocity change.
D. Velocity is directed towards the center of circle.

Explanation

To solve the problem, we need to analyze the motion of a car moving in a circular path. The car describes equal angles in equal intervals of time, which indicates that it is moving with uniform angular velocity. Let's break down the solution step by step.

### Step 1: Understanding Circular Motion
The car is moving along a circular path. In circular motion, the object travels around a fixed point (the center of the circle) and maintains a constant distance (the radius) from that center.

**Hint:** Remember that in circular motion, the radius remains constant.

### Step 2: Angular Displacement and Angular Velocity
Since the car describes equal angles in equal intervals of time, it has a constant angular velocity (ω). Angular velocity is defined as the angle covered per unit time.

**Hint:** Angular velocity (ω) is given by the formula: ω = Δθ / Δt, where Δθ is the angular displacement and Δt is the time interval.

### Step 3: Linear Velocity
The linear velocity (v) of the car can be related to angular velocity using the formula:
\[ v = r \cdot \omega \]
where \( r \) is the radius of the circular path. Since \( r \) is constant and \( ω \) is constant, the linear velocity \( v \) is also constant.

**Hint:** Linear velocity can be calculated using the relationship between linear and angular velocity.

### Step 4: Direction of Velocity
Although the magnitude of the linear velocity is constant, the direction of the velocity vector changes continuously as the car moves along the circular path. The velocity vector is always tangent to the circular path at any given point.

**Hint:** The direction of the velocity vector is always tangent to the circle, which means it changes direction even though its magnitude remains the same.

### Step 5: Evaluating the Options
Now, let's evaluate the given options:
1. **Velocity is constant.** - This is incorrect because the direction of the velocity changes.
2. **Magnitude of velocity is constant.** - This is correct; the speed (magnitude of velocity) remains constant while the direction changes.
3. **Both magnitude and the direction of the velocity changes.** - This is incorrect; only the direction changes.
4. **Velocity is directed towards the center of the circle.** - This is incorrect; the velocity is directed tangentially to the circle, not towards the center.

### Conclusion
The correct statement about the velocity of the car is that the **magnitude of the velocity is constant, but the direction changes**. Therefore, the answer is option 2.

**Final Answer:** The magnitude of velocity is constant, but the direction changes.

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