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 𝑠 after 𝑡 seconds is given by 𝑠 = (2𝑡² − 3𝑡 + 3) m, where 𝑡 > 0. Determine the velocity, 𝑣, as a function of time.

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Video Transcript

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

We are told in the question that the displacement of a particle 𝑠 is equal to two 𝑡 squared minus three 𝑡 plus three meters. And we need to find an expression for the velocity 𝑣. In order to do this, we will need to differentiate our function, as 𝑣 of 𝑡 is equal to d by d𝑡 of 𝑠 of 𝑡. 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 𝑡 squared gives us 4𝑡. Differentiating negative three 𝑡 gives us negative three. And differentiating a constant, in this case three, gives us zero. The velocity is therefore equal to 4𝑡 minus three. As we are differentiating with respect to 𝑡, 𝑣 is equal to 4𝑡 minus three meters per second. This is an expression for the velocity as a function of time.