Video Transcript
A particle is moving in a straight line such that its acceleration 𝑎 is equal to
negative three meters per second squared and its initial velocity is 39 meters per
second. Find its displacement during the time interval from 𝑡 equals one to 𝑡 equals nine
seconds.
In order to solve this problem, we will use one of the equations of motion or SUVAT
equations. 𝑠 is equal 𝑢𝑡 plus half 𝑎𝑡 squared, where 𝑠 is the displacement, 𝑢 is the
initial velocity, 𝑡 is the time, and 𝑎 is the acceleration of the particle. We need to calculate the displacement 𝑠 between 𝑡 equals one and 𝑡 equals
nine.
In order to calculate this displacement 𝑠, we will firstly work out 𝑠 one, the
displacement between 𝑡 equals naught and 𝑡 equals one. We will then calculate 𝑠 two, the displacement between 𝑡 equals nought and 𝑡
equals nine. Subtracting these two answers will give us our value of 𝑠. If we consider the time between 𝑡 equals zero and 𝑡 equals one, 𝑢 is equal to 39
meters per second. 𝑎 is equal to negative three meters per second squared. 𝑡 is equal to one. And 𝑠 one is our unknown.
Substituting these values into the equation 𝑠 equals 𝑢𝑡 plus half 𝑎𝑡 squared
gives us 39 multiplied by one plus a half multiplied by negative three multiplied by
one squared. This is equal to 37.5. Therefore, the displacement from 𝑡 equals zero to 𝑡 equals one is 37.5 meters. In order to calculate the displacement 𝑠 two between the time 𝑡 equals zero and 𝑡
equals nine, our value for 𝑢, the initial velocity, is still 39. 𝑎 is equal to negative three and 𝑡 is equal to nine.
Substituting these values into our equation gives us 39 multiplied by nine plus a
half multiplied by negative three multiplied by nine squared. Therefore, 𝑠 two is equal to 229.5. The displacement of the particle from 𝑡 equals
zero to 𝑡 equals nine is 229.5 meters.
In order to calculate 𝑠, the displacement doing a time interval from 𝑡 equals one
to 𝑡 equals nine, we need to subtract 𝑠 one from 𝑠 two. 𝑠 is equal to 229.5 minus 37.5. This is equal to 192. Therefore, the displacement of the particle during the time interval is 192
meters.
