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Question Video: Determining Average Velocity for a Uniformly Accelerating Body Physics • 9th Grade

A body started moving from rest with uniform acceleration. Its velocity reached 12 m/s by the end of the sixth second. Find its average velocity when it has moved a distance of 16 m.

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Video Transcript

A body started moving from rest with uniform acceleration. Its velocity reached 12 meters per seconds by the end of the sixth second. Find its average velocity when it has moved a distance of 16 meters.

In this question, we want to calculate the body’s average velocity when it has moved a distance of 16 meters. We are told that the body is moving with a uniform acceleration. So we can recall an equation that calculates the acceleration of an object. This equation is given by 𝑎 equals 𝑣 minus 𝑢 over 𝑡, where 𝑎 is the acceleration, 𝑣 is the final velocity, 𝑢 is the initial velocity, and 𝑡 is the time interval.

We are told in the question that the object starts at rest, meaning that the object’s initial velocity is zero. So 𝑢 equals zero meters per second. The object reaches a velocity of 12 meters per second after six seconds. So 𝑣 equals 12 meters per second and 𝑡 equals six seconds. Substituting these values into the equation for acceleration, we find that the acceleration of the object is equal to 12 meters per second minus zero meters per second over six seconds, which equals two meters per second squared.

Now that we have a value for the acceleration of the object, we can recall an equation of motion that describes uniformly accelerated straight motion. This equation is given by 𝑠 equals 𝑢𝑡 plus half 𝑎𝑡 squared, where 𝑠 is the displacement, 𝑢 is the initial velocity, 𝑎 is the acceleration, and 𝑡 is the time interval. We want to calculate the time taken for the object to move a distance of 16 meters. This means that 𝑠 is equal to 16 meters.

We have the values for the initial velocity 𝑢 and the acceleration 𝑎. So we can substitute these values into this equation to find that 16 meters equals zero meters per second multiplied by 𝑡 plus one-half multiplied by two meters per second squared multiplied by 𝑡 squared. The right-hand side simplifies to 𝑡 squared. So we can take the square root of both sides to find that 𝑡 equals four seconds. This is the time taken for the object to move a distance of 16 meters.

We can now calculate the average velocity using the equation 𝑣 average equals Δ𝑥 over Δ𝑡, where Δ𝑥 is the change in distance and Δ𝑡 is the change in time. The change in distance is 16 meters, and the change in time is four seconds. So the average velocity is equal to 16 meters over four seconds, which equals four meters per second. And thus, we have arrived at our answer. The average velocity of the object is four meters per second when it has moved a distance of 16 meters.

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