# Question Video: Finding the Velocity of a Particle Accelerating in the Negative Direction after a Given Time Mathematics

If a particle which was moving in a straight line with an initial velocity 𝑣₀ started decelerating at a rate of 10 m/s² such that it came to rest 5 seconds later, what would the body’s velocity be 6 seconds after it started decelerating? Let the direction of the initial velocity be the positive direction.

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### Video Transcript

If a particle which was moving in a straight line with an initial velocity 𝑣 sub zero started decelerating at a rate of 10 meters per second squared such that it came to rest five seconds later, what would the body’s velocity be six seconds after it started decelerating? Let the direction of the initial velocity be the positive direction.

In order to answer this question, we will use the equations of uniform acceleration, known as the SUVAT equations. 𝑠 is the displacement of the particle, 𝑢 its initial velocity, 𝑣 the final velocity, 𝑎 the acceleration, and 𝑡 the time. Our initial thoughts here might be that this is a two-part question where we firstly need to calculate the initial velocity 𝑣 sub zero. However, there is an alternative method we can use by just considering the final second of the body’s motion.

We will consider the motion of the particle between 𝑡 equals five seconds and 𝑡 equals six seconds. The time between these two points is one second. Therefore, 𝑡 is one second. We know that the body was at rest when 𝑡 was equal to five seconds. Therefore, the initial velocity for this one-second period is zero meters per second. We are also told that the particle moves with a constant deceleration of 10 meters per second squared. This means that our value for 𝑎, acceleration, is negative 10.

We are trying to calculate the value of 𝑣, which is the body’s velocity after six seconds. In order to do this, we will use the equation 𝑣 is equal to 𝑢 plus 𝑎𝑡. Substituting in our values, we have 𝑣 is equal to zero plus negative 10 multiplied by one. This gives us a value of 𝑣 equal to negative 10. We can therefore conclude that the body’s velocity six seconds after it started decelerating is negative 10 meters per second. This means that it is moving with a speed of 10 meters per second in the negative direction.