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.
