Video Transcript
Motorcycles A and B are moving in a
straight line. The speed of A changes from 20
meters per second to 24 meters per second in two seconds, while the speed of B
changes from three meters per second to 10 meters per second in four seconds. Choose the correct statement from
the following. (A) The acceleration of A is twice
that of B. (B) The acceleration of B is triple
that of A. (C) The displacement of A in two
seconds is greater than the displacement of B in four seconds. (D) The average speed of B in four
seconds is greater than the average speed of A in two seconds.
In this question, we have two
motorcycles moving in a straight line and we want to determine which of the
statements are correct.
Let’s consider the first two
options. Options (A) and (B) compare the
acceleration of the two motorcycles. We can recall that the acceleration
of an object is given by the equation 𝑎 equals 𝑣 minus 𝑢 over 𝑡, where 𝑣 is the
final velocity, 𝑢 is the initial velocity, and 𝑡 is the time interval. These are vector quantities. But since the motorcycles are
moving in a straight line and do not change direction, we only need to consider the
magnitudes of these values. So let’s calculate the acceleration
for both motorcycles.
For motorcycle A, the initial
velocity is given as 20 meters per second. So we can write 𝑢 A equals 20
meters per second. The final velocity is given as 24
meters per second. So we can write 𝑣 A equals 24
meters per second. And this change in speed happens
over two seconds. So we can write the time interval
𝑡 A equals two seconds. Substituting these values into the
equation for acceleration, we find that the acceleration of motorcycle A is equal to
24 meters per second minus 20 meters per second over two seconds, which equals two
meters per second squared.
For motorcycle B, the initial
velocity is given as three meters per second. So we can write 𝑢 B equals three
meters per second. The final velocity is given as 10
meters per second. So we can write 𝑣 B equals 10
meters per second. And this change in speed happens
over four seconds. So we can write the time interval
𝑡 B equals four seconds. Substituting these values into the
equation for acceleration, we find that the acceleration of motorcycle B is equal to
10 meters per second minus three meters per second over four seconds, which equals
1.75 meters per second squared.
We can now compare the
accelerations for both motorcycles. If we perform the calculation 𝑎 A
over 𝑎 B, we find that this is equal to 1.14. So the acceleration of A is 1.14
times that of B, which means that option (A) is incorrect. If we perform the calculation 𝑎 B
over 𝑎 A, we find that this is equal to 0.88. So the acceleration of B is 0.88
times that of A, which means that option (B) is incorrect.
So let’s consider option (C). 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 have the values for the initial
velocity, acceleration, and time interval for both motorcycles. So we can substitute in these
values to calculate the displacements for both motorcycles.
Let’s clear options (A) and (B)
since we know they are incorrect so that we have more space to work with. The displacement of motorcycle A is
given by 20 meters per second multiplied by two seconds plus one-half multiplied by
two meters per second squared multiplied by two seconds squared, which equals 44
meters. The displacement of motorcycle B is
given by three meters per second multiplied by four seconds plus one-half multiplied
by 1.75 meters per second squared multiplied by four seconds squared, which equals
26 meters.
Comparing the two displacements, we
see that the displacement of motorcycle A is greater than the displacement of
motorcycle B. So it looks like option (C) is the
correct answer.
Just to be sure, let’s consider
option (D). We can calculate the average
velocity using the equation 𝑣 average equals 𝑣 plus 𝑢 over two. Now let’s calculate the average
speed of both motorcycles. The average speed of motorcycle A
is equal to 24 meters per second plus 20 meters per second over two, which is equal
to 22 meters per second. The average speed of motorcycle B
is equal to 10 meters per second plus three meters per second over two, which is
equal to 6.5 meters per second.
Comparing the average speeds of
both motorcycles, we see that the average speed of motorcycle B in four seconds is
less than the average speed of motorcycle A in two seconds. So option (D) is incorrect.
Thus, we can be sure that option
(C) is the correct answer. The displacement of A in two
seconds is greater than the displacement of B in four seconds.
