A car going initially with a velocity 13.5 m / s accelerates at a rate of 1.9 m / s^2 for 6.2

A car going initially with a velocity 13.5 m / s...

Key Concepts

Displacement and Time Calculations

Calculating displacement and cumulative time in motion problems entails applying suitable kinematic formulas to each segment of the movement. By finding the displacement and duration in each phase and then summing them appropriately, one can determine the overall distance traveled and the total time from start to stop.

Segmented Motion Analysis

Segmented motion analysis involves breaking down a motion event into distinct phases, each with its own acceleration or deceleration. This approach is crucial when different segments of the motion have different accelerations, such as an acceleration phase followed by a deceleration phase. By analyzing each segment separately and then combining the results, we can accurately determine overall characteristics like total distance traveled and total time.

Uniform Acceleration

Uniform acceleration refers to motion with a constant acceleration, meaning the rate of change of velocity remains fixed over time. This principle allows us to apply standard equations directly to analyze different aspects of the motion, such as velocity change, displacement, and time intervals, without accounting for variations in acceleration.

Kinematic Equations

Kinematic equations are fundamental formulas that relate displacement, initial velocity, final velocity, acceleration, and time in uniformly accelerated motion. These equations allow us to determine unknown variables when others are known, making them essential for solving problems involving motion under constant acceleration and deceleration.

Transcript

00:01 When we have a car that has an initial velocity of 13 .5 meters per second, and i'll then accelerate at a rate of 1 .9 meters per second squared.

00:16 And this acceleration happens for a time of 6 .2 seconds.

00:21 We'll call that t1.

00:23 After the acceleration part, the car will decelerate at a rate of negative 1 .2 meters per second squared.

00:33 And because of this deceleration part, the car will begin to slow down and eventually come to a stop.

00:39 So with this information, we want to find a few things.

00:43 First, we want to find its final velocity after the acceleration part.

00:49 So we can use kinematic equation, which is the final velocity.

00:53 So the velocity at the end of the acceleration part is equal to its initial velocity plus acceleration.

01:00 And here's the first acceleration part, times time t.

01:05 And so we know the initial velocity we know that it's acceleration and we know time so we just plug in all our values and we can get that final velocity for the acceleration part now in part b we want to find the total time from the beginning to the end of the whole trip so when it begins to accelerate decelerate and then come to a stop so we need to find the time it takes the deceleration part because we already know the time for the acceleration part, it's given as 6 .2 seconds.

01:39 So now we use another kinematic equation, which is final velocity, is equal to initial velocity plus two, plus acceleration, times t.

01:52 So the same one as part a.

01:53 Only this time we're dealing with deceleration and time t2, so another time.

02:01 And all we do is solve for time t2, since we know the deceleration part.

02:07 And in this case, the final velocity is actually zero because the car will eventually come to a stop.

02:15 That's its final velocity.

02:17 Its initial velocity is the velocity of the end of the acceleration part, which we'll find from part a.

02:25 And we can plug that in and solve for t2.

02:28 And once we have that, we add it to the time of the acceleration part, and we get our total time.

02:34 And then for part c to find the total distance or how far this car has traveled, we need to find the distance for the acceleration part and the deceleration part.

02:48 With acceleration part, we can use x is equal to initial velocity or v1 times time t, plus one half times acceleration part times t1 squared.

03:06 And here all we have to do is plug in our values and we find the distance the car travels for the acceleration part.

03:14 And for the deceleration part, we use a separate kinematic equation, which is the final velocity squared is equal to initial velocity squared plus two times the deceleration part, a2, times the distance it travels in the deceleration part.

03:34 So we can call this x2.

03:36 And x1 will be the distance for the acceleration part...

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