### Video Transcript

A particle is moving in a straight line such that its acceleration π 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 π‘ equals one to π‘ equals nine
seconds.

In order to solve this problem, we will use one of the equations of motion or SUVAT
equations. π is equal π’π‘ plus half ππ‘ squared, where π is the displacement, π’ is the
initial velocity, π‘ is the time, and π is the acceleration of the particle. We need to calculate the displacement π between π‘ equals one and π‘ equals
nine.

In order to calculate this displacement π , we will firstly work out π one, the
displacement between π‘ equals naught and π‘ equals one. We will then calculate π two, the displacement between π‘ equals nought and π‘
equals nine. Subtracting these two answers will give us our value of π . If we consider the time between π‘ equals zero and π‘ equals one, π’ is equal to 39
meters per second. π is equal to negative three meters per second squared. π‘ is equal to one. And π one is our unknown.

Substituting these values into the equation π equals π’π‘ plus half ππ‘ 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 π‘ equals zero to π‘ equals one is 37.5 meters. In order to calculate the displacement π two between the time π‘ equals zero and π‘
equals nine, our value for π’, the initial velocity, is still 39. π is equal to negative three and π‘ 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, π two is equal to 229.5. The displacement of the particle from π‘ equals
zero to π‘ equals nine is 229.5 meters.

In order to calculate π , the displacement doing a time interval from π‘ equals one
to π‘ equals nine, we need to subtract π one from π two. π 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.