Question

Determine the displacement , velocity, and the acceleration of an object at t=2s . if displacement x=(5t^3 -12t^2+6t-7 )m​

Answer 1

Answer:

displacement =

$5 {t}^{2} - 12 {t}^{2} + 6t - 7$

velocity=

$15 {t}^{2} - 24t + 6$

acceleration =

$30t - 24$

I HOPE YOU UNDERSTOOD

Answer 2

Answer :

Displacement = x = 5t³ - 12t² + 6t - 7

Differentiating x :

⇒ v = dx/dt

⇒ 3*5t² - 2*12t + 6 - 0

⇒ 15t² - 24t + 6

Now, Instantaneous velocity at 2 seconds :

⇒ 15*2² - 24*2 + 6

⇒ 15*4 - 48 + 6

⇒ 60 + 6 - 48

⇒ 66 - 48

⇒ 18 m/s

Hence, Instantaneous velocity at time of 2 seconds = 18 m/s.

Now, Finding Instantaneous acceleration :

Differentiating v :

⇒ a = dv/dt

⇒ d(15t² - 24t + 6)/dt

⇒ 2*15t - 24 + 0

⇒ 30t - 24

So, Instantaneous acceleration at t = 2 seconds :

⇒ 30*2 - 24

⇒ 60 - 24

⇒ 36 m/s²

Hence, Instantaneous Acceleration at time of 2 seconds = 36 m/s².

Some Additional Information -

• Speed is the distance travelled per unit time.

• Velocity is the displacement per unit time.

• Speed is a scalar quantity.

• Velocity is a vector quantity.

• Distance is the total length of the path travelled by the body.