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