Velocity Physics Example 3

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Example 3

medium
A particle's position is given by x(t)=3t2+2tx(t) = 3t^2 + 2t. What is the instantaneous velocity at t=4 st = 4 \text{ s}?

Solution

  1. 1
    Instantaneous velocity is the derivative of position: v(t)=dxdt=6t+2v(t) = \frac{dx}{dt} = 6t + 2.
  2. 2
    At t=4t = 4: v(4)=6(4)+2=26 m/sv(4) = 6(4) + 2 = 26 \text{ m/s}

Answer

v(4)=26 m/sv(4) = 26 \text{ m/s}
Instantaneous velocity is the rate of change of position at a specific moment. It is found by differentiating the position function with respect to time.

About Velocity

The rate of change of position with respect to time, including both magnitude and direction.

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More Velocity Examples

Example 1 easy

A car travels [formula] east in [formula]. What is its average velocity?

Example 2 medium

A cyclist rides [formula] north in [formula], then [formula] south in [formula]. What is the average

Example 4 medium

A car accelerates from [formula] to [formula] in [formula]. Find the average velocity.

Example 5 medium

A car drives [formula] north in [formula], then [formula] south in [formula]. Find: (a) average spee

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