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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?
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Let the direction of the initial velocity be the positive direction.
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In order to answer this question, we will use the equations of uniform acceleration, known as the SUVAT equations.
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𝑠 is the displacement of the particle, 𝑢 its initial velocity, 𝑣 the final velocity, 𝑎 the acceleration, and 𝑡 the time.
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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.
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However, there is an alternative method we can use by just considering the final second of the body’s motion.
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We will consider the motion of the particle between 𝑡 equals five seconds and 𝑡 equals six seconds.
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The time between these two points is one second.
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Therefore, 𝑡 is one second.
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We know that the body was at rest when 𝑡 was equal to five seconds.
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Therefore, the initial velocity for this one-second period is zero meters per second.
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We are also told that the particle moves with a constant deceleration of 10 meters per second squared.
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This means that our value for 𝑎, acceleration, is negative 10.
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We are trying to calculate the value of 𝑣, which is the body’s velocity after six seconds.
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In order to do this, we will use the equation 𝑣 is equal to 𝑢 plus 𝑎𝑡.
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Substituting in our values, we have 𝑣 is equal to zero plus negative 10 multiplied by one.
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This gives us a value of 𝑣 equal to negative 10.
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We can therefore conclude that the body’s velocity six seconds after it started decelerating is negative 10 meters per second.
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This means that it is moving with a speed of 10 meters per second in the negative direction.