### Video Transcript

Determine the time required for a particle to increase its velocity from seven meters per second to 18 meters per second over a distance of 269 meters, given that it is moving in a straight line with a uniform acceleration.

In order to answer this question, we will use the equations of uniform acceleration known as the SUVAT equations. 𝑠 is the displacement, 𝑢 the initial velocity, 𝑣 the final velocity, 𝑎 the acceleration, and 𝑡 the time. We are told that the initial velocity is seven meters per second. The final velocity is 18 meters per second. As the particle travels a distance of 269 meters, the displacement is 269 meters. We want to calculate the value of the time 𝑡.

In order to do this, we will use the equation 𝑠 is equal to 𝑢 plus 𝑣 divided by two multiplied by 𝑡. Substituting in our values, we have 269 is equal to seven plus 18 divided by two multiplied by 𝑡. Seven plus 18 is 25, and dividing this by two gives us 12.5. We can then divide both sides of this equation by 12.5, giving us 𝑡 is equal to 21.52. The time taken for the particle to increase its velocity from seven to 18 meters per second is 21.52 seconds.