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A particle moves along the x-axis so that at time t >= 0 its velocity is given by v(t)=-2t+6. Determine if the particle is moving to the right or to the left at t=10.

A particle moves along the x x -axis so that at time t≥0 t \geq 0 its velocity is given by v(t)=−2t+6 v(t)=-2 t+6 . Determine if the particle is moving to the right or to the left at t=10 t=10 .

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Relate position, velocity, speed, and acceleration using derivativesright chevron icon

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Q. A particle moves along the x x -axis so that at time t≥0 t \geq 0 its velocity is given by v(t)=−2t+6 v(t)=-2 t+6 . Determine if the particle is moving to the right or to the left at t=10 t=10 .
  1. Identify function and time: Identify the given velocity function and the specific time at which we need to determine the direction of the particle's movement.\newlineThe velocity function is given by v(t)=−2t+6v(t) = -2t + 6, and we need to find the direction of movement at t=10t = 10.
  2. Plug in value: Plug the value of t=10t = 10 into the velocity function to find the velocity at that time.\newlinev(10)=−2(10)+6=−20+6=−14v(10) = -2(10) + 6 = -20 + 6 = -14
  3. Analyze velocity sign: Analyze the sign of the velocity at t=10t = 10.\newlineSince v(10)=−14v(10) = -14, which is negative, this indicates that the particle is moving to the left along the x-axis at t=10t = 10.

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