A fullback preparing to carry the football starts from rest and accelerates straight ahead. He is handed the ball just before he reaches the line of scrimmage. Assume that the fullback accelerates uniformly (even during the handoff), reaching the line with a velocity of 7.96 m/s. If he takes 1.18 s to reach the line, how far behind it did he start?
Can I assume that acceleration is 0? If yes then I can use the x=v=Vi*t + 1/2at^2 equation. If not, I have no idea where to start.
NO!!!!
You assume that the acceleration, a, is CONSTANT.
v = 0 + a t
at t = 1.18 s
v = 7.96 m/s
so
7.96 = a (1.18)
a = 7.96/1.18
NOW
use x = 0 + 0 + (1/2) a t^2
No, you cannot assume that the acceleration is 0 in this case. The problem states that the fullback accelerates uniformly, meaning that his acceleration is constant throughout the entire motion, including during the handoff.
To solve this problem, you can use the equations of motion. The equation you mentioned, x = v*t + (1/2)*a*t^2, is one of these equations.
To start, let's assign the values given in the problem to their respective variables:
- v (final velocity) = 7.96 m/s
- t (time taken) = 1.18 s
- a (acceleration) = unknown
- x (initial position) = unknown
We need to find the initial position of the fullback, which is represented by x.
The equation that relates these variables is:
x = v*t + (1/2)*a*t^2
Since we are given the values of v and t, we can substitute them into the equation:
x = (7.96 m/s) * (1.18 s) + (1/2) * a * (1.18 s)^2
Now, let's solve for x:
x = 9.4064 m + (0.5) * a * 1.3924 s^2
To solve for x, we need to find the value of a, which represents the acceleration.
The problem states that the fullback starts from rest, which means his initial velocity (Vi) is 0 m/s. Since we know the final velocity is 7.96 m/s and the time taken is 1.18 s, we can use the equation:
v = Vi + a*t
7.96 m/s = 0 m/s + a * 1.18 s
Simplifying this equation, we find:
a = 7.96 m/s / 1.18 s
a ≈ 6.7466 m/s^2
Now that we have the value of a, we can substitute it back into the first equation to solve for x:
x = 9.4064 m + (0.5) * 6.7466 m/s^2 * (1.3924 s)^2
Simplifying this equation will give us the distance behind the line of scrimmage that the fullback started from.