Question Video: Finding the Time Required for a Body Moving with a Uniform Acceleration to Come to Rest Mathematics

A particle started moving in a straight line at 7 m/s. Given that its acceleration was of magnitude 2 cm/sΒ² in the opposite direction to its movement, find the time taken for the particle to come to rest.

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Video Transcript

A particle started moving in a straight line at seven meters per second. Given that its acceleration was of magnitude two centimeters per second squared in the opposite direction to its movement, find the time taken for the particle to come to rest.

In order to answer this question, we will use the equations of constant acceleration, often known as the SUVAT equations. The 𝑠 stands for the displacement, the 𝑒 for the initial velocity, 𝑣 for the final velocity, π‘Ž acceleration, and 𝑑 the time. In this question, we are told that the initial velocity is seven meters per second. The particle has acceleration of magnitude two centimeters per second squared. However, this is in the opposite direction to its movement. We can therefore conclude that the particle is decelerating, and the acceleration is negative two centimeters per second squared.

We want to calculate the time for the particle to come to rest. This means that its final velocity is zero. We notice that our units are different. The velocities are given in meters per second, whereas the acceleration is in centimeters per second squared. We recall that there are 100 centimeters in a meter. This means that we can multiply our velocities by 100 to convert them into centimeters per second. The initial velocity is 700 centimeters per second, and the final velocity is zero centimeters per second.

The equation we will use in this question is 𝑣 equals 𝑒 plus π‘Žπ‘‘ as we want the equation that doesn’t include 𝑠. Substituting in our values, we have zero equals 700 plus negative two multiplied by 𝑑. This simplifies to 700 minus two 𝑑 is equal to zero. We can then add two 𝑑 to both sides of this equation. Finally, by dividing both sides by two, we get a value of 𝑑 equal to 350. The time taken for the particle to come to rest is 350 seconds.

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