the position of the particle is given by x is equal to 6tsquare - 2T + 3 Find its initial position , instantaneous velocity at 3 second , instantaneous acceleration at t is equal to 2 second , average velocity between t is equal to 2 seconds and t is equal to 3 seconds .
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Answers
Given :
Position equation of the particle is given by
- x = 6t² - 2t + 3
To Find :
- Initial position
- Instantaneous velocity at t = 3s
- Instantaneous acceleration at t = 2s
- Average velocity b/w t = 2 and 3s
Solution :
A] Position of particle at t = 0 s
In order to find position of particle, just put value of t in the given equation. Equation will give you the answer :)
➝ x = 6t² - 2t + 3
➝ x = 6(0)² -2(0) + 3
➝ x = 0 - 0 + 3
➝ x = 3 m
B] Velocity of particle at t = 3 s
In order to find velocity of the particle, we have to differentiate the given position equation wrt time.
➝ v = dx/dt
➝ v = d (6t² - 2t + 3) / dt
➝ v = 12t - 2
Putting t = 3, we get .....
➝ v = 12(3) - 2
➝ v = 36 - 2
➝ v = 34 m/s
C] Acceleration of particle at t = 2 s
In order to find acceleration of the particle, we have to differentiate velocity equation wrt time
➝ a = dv/dt
➝ a = d (12t - 2) / dt
➝ a = 12 m/s²
Particle has constant acceleration. It means, acceleration doesn't depend on time.
D] Average velocity b/w t = 2 and 3 s
Velocity of particle at 2 s :
➝ v = 12t - 2
➝ v = 12(2) - 2
➝ v = 24 - 2
➝ v = 22 m/s
Velocity of particle at 3 s = 34 m/s
➝ Vav = (v₂ + v₃) / 2
➝ Vav = (22 + 34) / 2
➝ Vav = 56/2
➝ Vav = 28 m/s