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A body, moving in a straight line decelerated uniformly at a rate of six centimeters per second squared.
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Given that it came to rest in 27 seconds, determine its initial velocity.
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We will answer this question using our equations of uniform acceleration, known as the SUVAT equations.
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𝑠 is the displacement of the body, 𝑢 its initial velocity, 𝑣 the final velocity, 𝑎 the acceleration, and 𝑡 the time.
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In this question, the body is decelerating, which means that 𝑎 will be negative.
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It is equal to negative six centimeters per second squared.
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The body comes to rest; therefore, 𝑣 is equal to zero centimeters per second.
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The time taken for it to come to rest is 27 seconds.
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We need to calculate the initial velocity 𝑢.
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We will do this using the equation 𝑣 is equal to 𝑢 plus 𝑎𝑡.
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Substituting in our values, we get zero is equal to 𝑢 plus negative six multiplied by 27.
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This simplifies to zero is equal to 𝑢 minus 162.
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Adding 162 to both sides gives us 𝑢 is 162.
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The initial velocity of the body is, therefore, equal to 162 centimeters per second.