A cyclist, moving in a straight line, accelerated over a distance of 35.5 meters until his velocity reached 10.8 meters per second. Given that this took five seconds, find the cyclist’s initial velocity.
We can answer this question using our equations of uniform acceleration known as the SUVAT equations. 𝑠 indicates the displacement, 𝑢 the initial velocity, 𝑣 the final velocity, 𝑎 the acceleration, and 𝑡 the time. We are told that the cyclist covers a distance of 35.5 meters. This means that his displacement is 35.5. He reaches a velocity of 10.8 meters per second. So this is our value of 𝑣. As the time taken was five seconds, 𝑡 is equal to five.
We need to calculate the initial velocity 𝑢. We will use the equation 𝑠 is equal to 𝑢 plus 𝑣 divided by two multiplied by 𝑡. Substituting in our values, we have 35.5 is equal to 𝑢 plus 10.8 divided by two all multiplied by five. We can divide both sides of this equation by five such that 7.1 is equal to 𝑢 plus 10.8 divided by two. Multiplying by two, we have 14.2 is equal to 𝑢 plus 10.8. Finally, subtracting 10.8 from both sides of this equation gives us 𝑢 is equal to 3.4. The cyclist’s initial velocity is 3.4 meters per second.