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A particle moves in a straight line. Its position is defined by the equation x = 6t2 − t3 where t in seconds and x is in meters. The maximum velocity of the particle during its motion will be
- a)12 m/s
- b)6 m/s
- c)24 m/s
- d)48 m/s
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A particle moves in a straight line. Its position is defined by the eq...
The velocity of the particle is defined as the rate of change of its displacement and can be expressed as
v = dx/dt
whereas, the speed of the particle at any instance is given as the rate of change of its distance.
for maximum velocity
dv/dt = 0
Calculation:
Given :
Position: x= 6t2 - t3
dx/dt = V = 12t - 3t2 ...(i)
and for maximum velocity
dv/dt = 0,
dv/dt = 12-6t = 0 or 6t = 12 or t = 2 sec
Substitute this value of t in the (i)
we get v = 12× 2 - 3× 22 = 12 m/sec
v = dx/dt
whereas, the speed of the particle at any instance is given as the rate of change of its distance.
for maximum velocity
dv/dt = 0
Calculation:
Given :
Position: x= 6t2 - t3
dx/dt = V = 12t - 3t2 ...(i)
and for maximum velocity
dv/dt = 0,
dv/dt = 12-6t = 0 or 6t = 12 or t = 2 sec
Substitute this value of t in the (i)
we get v = 12× 2 - 3× 22 = 12 m/sec
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Community Answer
A particle moves in a straight line. Its position is defined by the eq...
The equation x = 6t^2 describes the position of the particle in terms of time, t.
In this equation, x represents the position of the particle and t represents the time elapsed. The position of the particle changes as time progresses. The function 6t^2 describes how the position changes with time.
To find the position of the particle at a specific time, substitute the value of t into the equation. For example, if t = 2, then x = 6(2)^2 = 6(4) = 24. This means that the particle's position at t = 2 is 24.
The equation x = 6t^2 describes the motion of the particle in a straight line. As time increases, the position of the particle increases quadratically. This means that the particle is accelerating, as the position changes at an increasing rate.
In this equation, x represents the position of the particle and t represents the time elapsed. The position of the particle changes as time progresses. The function 6t^2 describes how the position changes with time.
To find the position of the particle at a specific time, substitute the value of t into the equation. For example, if t = 2, then x = 6(2)^2 = 6(4) = 24. This means that the particle's position at t = 2 is 24.
The equation x = 6t^2 describes the motion of the particle in a straight line. As time increases, the position of the particle increases quadratically. This means that the particle is accelerating, as the position changes at an increasing rate.
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A particle moves in a straight line. Its position is defined by the equation x = 6t2 − t3 where t in seconds and x is in meters. The maximum velocity of the particle during its motion will bea)12 m/sb)6 m/sc)24 m/sd)48 m/sCorrect answer is option 'A'. Can you explain this answer?
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