Question Video: Determining the Velocity of a Particle That Moves in a Straight Line given Its Displacement as a Function of Time | Nagwa Question Video: Determining the Velocity of a Particle That Moves in a Straight Line given Its Displacement as a Function of Time | Nagwa

Question Video: Determining the Velocity of a Particle That Moves in a Straight Line given Its Displacement as a Function of Time Mathematics

A particle is moving in a straight line such that its displacement ๐  after ๐ก seconds is given by ๐  = (2๐กยฒ โ 3๐ก + 3) m, where ๐ก > 0. Determine the velocity, ๐ฃ, as a function of time.

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Video Transcript

A particle is moving in a straight line such that its displacement ๐  after ๐ก seconds is given by ๐  is equal to two ๐ก squared minus three ๐ก plus three meters, where ๐ก is greater than zero. Determine the velocity ๐ฃ as a function of time.

We are told in the question that the displacement of a particle ๐  is equal to two ๐ก squared minus three ๐ก plus three meters. And we need to find an expression for the velocity ๐ฃ. In order to do this, we will need to differentiate our function, as ๐ฃ of ๐ก is equal to d by d๐ก of ๐  of ๐ก. If the displacement of a body is given as a function in terms of time, we can differentiate to find an expression for the velocity. Differentiating two ๐ก squared gives us 4๐ก. Differentiating negative three ๐ก gives us negative three. And differentiating a constant, in this case three, gives us zero. The velocity is therefore equal to 4๐ก minus three. As we are differentiating with respect to ๐ก, ๐ฃ is equal to 4๐ก minus three meters per second. This is an expression for the velocity as a function of time.