Question

The position function of an object is x(t)=t²-3t. Compute the instantaneous velocity of object at t=7s.​

Answer 1

Answer:

• Velocity of object at the given instant t will be 11 m/s .

Explanation:

Given :

• position function of an object as ; x(t) = t² - 3 t

To find :

• instantaneous velocity of object at t = 7 s ; v ( t ) = ?

Knowledge required :

• Instantaneous velocity of any object is given as the derivative of position of object with respect to time at a given instant.

$\red{\bigstar}\:\;\;\;\boxed{\sf{v(t)=\dfrac{d(x)}{d(t)}}}$

Solution :

Using the formula to calculate instantaneous velocity

$\red{\longrightarrow}\;\;\sf{v(t)=\dfrac{d(x)}{d(t)}}$

$\red{\longrightarrow}\;\;\sf{v(t)=\dfrac{d\;x}{d\;t}=\dfrac{d(t^2-3t)}{d\;t}}$

differentiating

$\red{\longrightarrow}\;\;\sf{v(t)=2t-3}$

therefore,

• velocity of object at an instant of time 't' will be 2 t - 3

so,

velocity of object at t = 7 will be

$\red{\longrightarrow}\sf{v(7)=2(7)-3}$

$\red{\longrightarrow}\sf{v(7)=14-3}$

$\red{\longrightarrow}\sf{v(7)=11}$

therefore,

• Velocity of object at an instant, t = 7 sec will be 11 m/s .

Answer 2

Given ,

The position function of an object is

• x(t) = (t)² - 3t

As we know that ,

The instanteous velocity of object is given by

$\boxed{ \tt{Instanteous \: velocity \: = \frac{dx}{dt} }}$

Thus ,

$\sf \mapsto v(t) = \frac{d \{ {(t)}^{2} - 3t \} }{dt}$

$\sf \mapsto v(t) = \frac{d {(t)}^{2} }{dt} - \frac{d(3t)}{t}$

$\sf \mapsto v(t) = 2t - 3$

Put t = 7 in above equation , we get

v(7) = 2(7) - 3

v(7) = 14 - 3

v(7) = 11 m/s

Therefore , the instantaneous velocity of object at t = 7 sec is 11 m/s