The acceleration 'a' in m/s2 of a particle is given by a = 3t2 + 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 :12 m/s18 m/s27 m/s36 m/s
Question
The acceleration 'a' in m/s2 of a particle is given by a = 3t2 + 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 :12 m/s18 m/s27 m/s36 m/s
Solution
The velocity of a particle at any time can be found by integrating the acceleration function with respect to time.
The acceleration function is given as a = 3t^2 + 2t + 2.
To find the velocity function, we integrate the acceleration function:
∫a dt = ∫(3t^2 + 2t + 2) dt = t^3 + t^2 + 2t + C
The constant of integration, C, can be found using the initial condition that the velocity u = 2 m/s at t = 0. Substituting these values in:
2 = 0 + 0 + 0 + C C = 2
So the velocity function is v = t^3 + t^2 + 2t + 2.
To find the velocity at the end of 2 seconds, we substitute t = 2 into the velocity function:
v = 2^3 + 2^2 + 2*2 + 2 = 8 + 4 + 4 + 2 = 18 m/s
So, the velocity at the end of 2 seconds will be 18 m/s.
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