The distance travelled by a particle is related to time t as `x = 4x^2` . The velocity of the particle at t = 5s

Options

A. `8ms^(-1)`
B. `20ms^(-1)`
C. `25ms^(-1)`
D. `40ms^(-1)`

Answer

To solve the problem, we need to find the velocity of a particle whose distance travelled \( x \) is related to time \( t \) by the equation \( x = 4t^2 \).

### Step-by-Step Solution:

1. **Identify the relationship**: We have the equation given as:
\[ x = 4t^2 \]

2. **Differentiate with respect to time**: To find the velocity \( v \), we differentiate \( x \) with respect to \( t \):
\[ v = \frac{dx}{dt} = \frac{d}{dt}(4t^2) \]

3. **Apply the power rule of differentiation**: Using the power rule, we differentiate:
\[ v = 4 \cdot 2t^{2-1} = 8t \]

4. **Substitute the given time**: Now, we need to find the velocity at \( t = 5 \) seconds:
\[ v = 8 \cdot 5 = 40 \, \text{m/s} \]

5. **Final answer**: Therefore, the velocity of the particle at \( t = 5 \) seconds is:
\[ v = 40 \, \text{m/s} \]

### Summary:
The velocity of the particle at \( t = 5 \) seconds is \( 40 \, \text{m/s} \).