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

The instantaneous velocity at t=2 is 80

Step-by-step 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 = (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) = (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