Question

x=(2t-3)^2

v=dx/dt =?


plz do solve

with proper explanation

Answer 1

Answer:

To find velocity Differentiate Above Function With respect to time.

As dx/dt = v

Above function will become equation for velocity.

Put the Values of time In the above velocity Function to get Velocity of the particle at that time instant.

Thanks for asking.

Answer 2

$\huge{\underline{\underline{\sf{Answer \colon}}}}$

From the Question,

"x" is defined the relation:

$\sf{x = (2t - 3) {}^{2} } \\ \\ \implies \: \boxed{ \sf{x = 4t{}^{2} - 12t + 9 }}$

To find the velocity of the particle

Differentiating v w.r.t to t,we get:

$\sf{v = \frac{dx}{dt} } \\ \\ \rightarrow \: \sf{v = \frac{d(4t {}^{2} - 12t + 9)}{dt} } \\ \\ \: \huge{ \rightarrow \: \: \underline{\boxed{ \sf{v = 8t - 12}}}}$

Velocity of the particle during the whole time interval is defined by the function: v = 8t - 12