Some informations are given for a body moving in a straight line. The body starts its motion at `t=0`.
Information I : The velocity of a body at the end of `4s` is `16 m//s`
Information II : The velocity of a body at the end of `12s` is `48 m//s`
Information III : the velocity of a body at the end of `22s` is `88 m//s`
The body is certainly moving with

Options

A. Uniform velocity
B. Uniform speed
C. Uniform acceleration
D. Data insufficient for generalization

Explanation

To determine the motion of the body based on the given information, we can analyze the velocities at different times and calculate the acceleration. Here’s a step-by-step solution:

### Step 1: Gather the given information
- Velocity at \( t = 4 \, \text{s} \): \( v_1 = 16 \, \text{m/s} \)
- Velocity at \( t = 12 \, \text{s} \): \( v_2 = 48 \, \text{m/s} \)
- Velocity at \( t = 22 \, \text{s} \): \( v_3 = 88 \, \text{m/s} \)

### Step 2: Calculate acceleration using the formula
The formula for acceleration \( a \) when the initial velocity \( u \) is assumed to be \( 0 \) (starting from rest) is:

\[ a = \frac{v}{t} \]

### Step 3: Calculate acceleration for each time interval

1. **For the first interval (0 to 4 seconds)**:
\[ a_1 = \frac{v_1}{t_1} = \frac{16 \, \text{m/s}}{4 \, \text{s}} = 4 \, \text{m/s}^2 \]

2. **For the second interval (0 to 12 seconds)**:
\[ a_2 = \frac{v_2}{t_2} = \frac{48 \, \text{m/s}}{12 \, \text{s}} = 4 \, \text{m/s}^2 \]

3. **For the third interval (0 to 22 seconds)**:
\[ a_3 = \frac{v_3}{t_3} = \frac{88 \, \text{m/s}}{22 \, \text{s}} = 4 \, \text{m/s}^2 \]

### Step 4: Analyze the results
From the calculations, we see that the acceleration \( a \) is consistently \( 4 \, \text{m/s}^2 \) for all time intervals. This indicates that the body is experiencing uniform acceleration.

### Step 5: Conclusion
Since the acceleration is constant, we can conclude that the body is moving with uniform acceleration. However, since the initial velocity \( u \) was not specified in the problem, we cannot definitively state the nature of the motion (whether it is uniform velocity or uniform speed). Therefore, the correct answer is that the data is insufficient for generalization.

### Final Answer:
The body is certainly moving with **insufficient data for generalization**.

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