A body moves in a straight line along Y-axis. Its distance y in metre) from the origin is given `y = 8t -3t^(2).` The average speed in the time interval from `t =0` second to `t =1` second is

Options

A. `-4 ms^(-1)`
B. Zero
C. `5ms^(-1)`
D. `6ms ^(-1)`

Answer

To find the average speed of the body moving along the Y-axis given the equation \( y = 8t - 3t^2 \), we will follow these steps:

### Step 1: Understand the average speed formula
The average speed is defined as the total distance traveled divided by the total time taken. Mathematically, it can be expressed as:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

### Step 2: Determine the time interval
We need to calculate the average speed from \( t = 0 \) seconds to \( t = 1 \) second. Therefore, the total time \( \Delta t \) is:

\[ \Delta t = 1 - 0 = 1 \text{ second} \]

### Step 3: Calculate the position at \( t = 0 \)
Substituting \( t = 0 \) into the equation \( y = 8t - 3t^2 \):

\[ y(0) = 8(0) - 3(0)^2 = 0 \text{ meters} \]

### Step 4: Calculate the position at \( t = 1 \)
Now, substituting \( t = 1 \) into the same equation:

\[ y(1) = 8(1) - 3(1)^2 = 8 - 3 = 5 \text{ meters} \]

### Step 5: Calculate the total distance traveled
The total distance traveled from \( t = 0 \) to \( t = 1 \) is:

\[ \text{Total Distance} = y(1) - y(0) = 5 - 0 = 5 \text{ meters} \]

### Step 6: Calculate the average speed
Now, we can calculate the average speed using the values we found:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{5 \text{ meters}}{1 \text{ second}} = 5 \text{ meters per second} \]

### Conclusion
Thus, the average speed of the body in the time interval from \( t = 0 \) seconds to \( t = 1 \) second is:

\[ \text{Average Speed} = 5 \text{ m/s} \]