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
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.