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 from \( t = 0 \) seconds to \( t = 1 \) second, we will follow these steps:

### Step 1: Determine the position at \( t = 0 \) seconds
We start with the given equation for distance:
\[ y = 8t - 3t^2 \]
Substituting \( t = 0 \):
\[ y(0) = 8(0) - 3(0)^2 = 0 \, \text{meters} \]

### Step 2: Determine the position at \( t = 1 \) second
Now, we substitute \( t = 1 \):
\[ y(1) = 8(1) - 3(1)^2 = 8 - 3 = 5 \, \text{meters} \]

### Step 3: Calculate the total distance traveled
The total distance traveled from \( t = 0 \) to \( t = 1 \) is:
\[ \text{Total distance} = y(1) - y(0) = 5 \, \text{meters} - 0 \, \text{meters} = 5 \, \text{meters} \]

### Step 4: Calculate the total time taken
The total time taken for this interval is:
\[ \text{Total time} = 1 \, \text{second} - 0 \, \text{seconds} = 1 \, \text{second} \]

### Step 5: Calculate the average speed
Average speed is defined as the total distance traveled divided by the total time taken:
\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{5 \, \text{meters}}{1 \, \text{second}} = 5 \, \text{meters/second} \]

Thus, the average speed of the body in the time interval from \( t = 0 \) seconds to \( t = 1 \) second is **5 meters/second**.

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