Video: Finding the Velocity of a Particle Moving with Uniform Acceleration at a Given Time

If a particle started moving in astraight line with an initial velocity of 25.1 cm/s and a uniform acceleration of 2.4 cm/s², determine its velocity after 9 seconds.

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Video Transcript

If a particle started moving in a straight line with an initial velocity of 25.1 centimeters per second and a uniform acceleration of 2.4 centimeters per square second, determine its velocity after nine seconds.

The question states that the particle has uniform acceleration. This is a good indication to us that we’re going to need to use the equations of uniform or constant acceleration. Those are the four kinematic equations. So, we begin by listing the equations out. Our job is to eliminate all but one of these equations. And we do so by listing the measurements that we’ve been given in the question. We’re given the initial velocity 𝑣 naught. That’s 25.1 centimeters per second. We’ve got an acceleration of 2.4 centimeters per square second and a time nine seconds.

We’re looking to calculate the velocity after nine seconds. Notice that that means we’re really not interested in Δ𝑥, the displacement of our object. And so, we go through and eliminate all of the equations that contain Δ𝑥. Those are two, equation three, and four. And so, we’re left with one equation; that’s 𝑣 equals 𝑣 naught plus 𝑎𝑡. Next, we substitute everything we know about our particle into this formula. We’re looking to calculate 𝑣, so we say that 𝑣 is equal to 𝑣 naught, which is 25.1, plus 𝑎 times 𝑡, that’s 2.4 times nine. 2.4 multiplied by nine is 21.6. So, velocity is given by 25.1 plus 21.6, which is 46.7.

Notice that we’ve been working in centimeters per second, centimeters per square second, and seconds. And so, the units for our velocity after nine seconds are centimeters per second. The velocity of the particle is therefore 46.7 centimeters per second.

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