Question

if the distance travelled by a body in the time t is given by x=t⁵ ,then what will be the instantaneous velocity of the body at t=2.​

Answer 1

Answer:

The instantaneous velocity at t=2 is 80

Explanation:

Instantaneous Velocity

The instantaneous velocity can be defined as the instant rate of change of the distance.

In calculus, it's computed as the derivative of the distance function. If x is the distance function x=f(t), then the instantaneous velocity is:

$\displaystyle v = \frac{dx}{dt}$

The distance traveled by a body in time t is given by:

$x(t)=t^5$

The instant velocity is:

$\displaystyle v(t) = \frac{d(t^5)}{dt}$

Applying the power rule:

$\displaystyle v(t) = 5t^4$

Evaluating at t=2

$\displaystyle v(2) = 5*2^4$

$\displaystyle v(2) = 5*16 = 80$

The instantaneous velocity at t=2 is 80