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The acceleration 'a' in m/s² of a particle is given by a = 3t^2 2t 2 where t is the time. If the particle starts out with a velocity. u = 2 m/s at t=0, then the velocity at the end of 2 seconds will be?
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The acceleration 'a' in m/s² of a particle is given by a = 3t^2 2t 2 w...
Velocity of a Particle with Given Acceleration
Given Information:
- Acceleration of a particle, a = 3t^2 2t^2 m/s²
- Initial velocity of a particle, u = 2 m/s
- Time, t = 2 seconds
Calculating Velocity:
Velocity of a particle can be calculated by integrating the acceleration function with respect to time.
∫a dt = ∫(3t^2 + 2t^2) dt
∫a dt = ∫5t^2 dt
∫a dt = (5t^3)/3 + C
where C is the constant of integration.
Using the initial condition, we can find the value of C.
At t=0, v=u=2 m/s
(5(0)^3)/3 + C = 2
C = 2
Therefore, the velocity function becomes:
v = (5t^3)/3 + 2
Calculating Velocity at t=2 seconds:
Substituting the value of t=2 seconds in the velocity function, we get:
v = (5(2)^3)/3 + 2 = 46.67 m/s
Conclusion:
The velocity of the particle at the end of 2 seconds is 46.67 m/s.
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The acceleration 'a' in m/s² of a particle is given by a = 3t^2 2t 2 where t is the time. If the particle starts out with a velocity. u = 2 m/s at t=0, then the velocity at the end of 2 seconds will be?
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