A particle moves in a circle of radius 10 cm. Its linear speed is given by v = 5t, where t is in seconds and v is in m/s. The tangential acceleration is:

1. Break Down the Problem

To find the tangential acceleration of the particle, we need to understand the relationship between linear speed and tangential acceleration. The linear speed is given by the equation $v = 5t$. We can find the tangential acceleration by differentiating the linear speed with respect to time.

2. Relevant Concepts

The tangential acceleration $a_t$ can be defined as the derivative of linear velocity $v$ with respect to time $t$: $a_t = \frac{dv}{dt}$

3. Analysis and Detail

Given: $v = 5t$ To find the tangential acceleration, differentiate $v$ with respect to $t$: $a_t = \frac{d(5t)}{dt} = 5$

4. Verify and Summarize

The tangential acceleration is constant at 5 m/s² because the velocity increases linearly with time.

Final Answer

The tangential acceleration of the particle is $5 \, \text{m/s}^2$.