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The acceleration a of a particle in m/s square is given by a=2t squ are + 3t +5 ,where the is the time . If the velocity of the particle at t=0 was 2 m/second then calculate it's velocity at t= 3 seconds ?
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The acceleration a of a particle in m/s square is given by a=2t squ a...
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The acceleration a of a particle in m/s square is given by a=2t squ a...
Given:
Acceleration (a) = 2t^3 + 3t^2 + 5
Initial velocity (u) = 2 m/s
Time (t) = 3 seconds

To find:
Velocity (v) at t = 3 seconds

Formula:
v = u + at

Calculation:
Given that the acceleration (a) is given by the equation 2t^3 + 3t^2 + 5.

At t = 0, the velocity (v) is 2 m/s. This gives us the initial velocity (u) of the particle.

At t = 3 seconds, we need to find the final velocity (v).

Using the formula v = u + at, we can substitute the values and calculate the final velocity.

Substituting the values:
u = 2 m/s
t = 3 seconds

v = u + at
v = 2 + (2t^3 + 3t^2 + 5)t

Simplifying the equation:
v = 2 + 2t^4 + 3t^3 + 5t
v = 2t^4 + 3t^3 + 5t + 2

Calculating the velocity at t = 3 seconds:
v = 2(3)^4 + 3(3)^3 + 5(3) + 2
v = 2(81) + 3(27) + 15 + 2
v = 162 + 81 + 15 + 2
v = 260 m/s

Conclusion:
The velocity of the particle at t = 3 seconds is 260 m/s.
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The acceleration a of a particle in m/s square is given by a=2t squ are + 3t +5 ,where the is the time . If the velocity of the particle at t=0 was 2 m/second then calculate it's velocity at t= 3 seconds ?
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