Question

A 103 kg fullback runs at the line of scrimmage.

(a) Find the constant force that must be exerted on him to bring him to rest in a distance of 1.1 m in a time interval of 0.30 s.
opposite the fullback's direction of motion

(b) How fast was he running initially?

Answer 1

Equation for average displacement:
Δx =[ (v₀ + v)t] / 2

Solve for initial velocity (v₀):

As final speed is zero, write v = 0 and solve the equation for initial velocity:
v₀ = 2Δx / t

Substitute given values
v₀ = 2 (1.1 m) / 0.30 s
= 7.33 m/s

use of the impulse-momentum theorem:
FΔt = Δp

Rearrange for force, F
F = Δp / Δt
= [m(v - v₀)] / t
= [103 kg( 0 - 7.33 m/s)] / 0.31s
= -2436.55 N

From the above calculations, the initial speed is 7.33 m/s