In a football game, the running back takes a handoff and begins running toward midfield at 3.21 yards/s. As he moves through his linemen, he accelerates at a rate of 1.71 yards/s^2 to a velocity of 7.54 yards/s before he is tackled. How far did he run after he got the ball?

Given Information:

Initial speed = u = 3.21 yards/s

Acceleration = α = 1.71 yards/s²

Final speed = v = 7.54 yards/s

Required Information:

Distance = s = ?

Answer:

Distance = s = 13.61

Explanation:

We are given the speeds and acceleration of the runner and we want to find out how much distance he covered before being tackled.

We know from the equations of motion,

v² = u² + 2αs

Where u is the initial speed of the runner, v is the final speed of the runner, α is the acceleration of the runner and s is the distance traveled by the runner.

Re-arranging the above equation for distance yields,

2αs = v² - u²

s = (v² - u²) / 2α

s = (7.54² - 3.21²) / 2*1.71

s = 46.55/3.42

s = 13.61 yards

Therefore, the runner traveled a distance of 13.61 yards before being tackled.