Answer:
vf = 12.51 m/s
Explanation:
Newton's second law to the grocery cart:
∑F = m*a Formula (1)
∑F : algebraic sum of the forces in Newton (N)
m : mass s (kg)
a : acceleration (m/s²)
We define the x-axis in the direction parallel to the movement of the grocery cart and the y-axis in the direction perpendicular to it.
Forces acting on the grocery cart
W: Weight of the block : In vertical direction downward
N : Normal force : In vertical direction upward
F : horizontal force
Calculated of the mas of the grocery cart (m)
W = m*g
m = W/g
W = 94.0 N , g = 9.81 m/s²
m = 94/9.81
m = 9.58 Kg
Calculated of the acceleration of the grocery cart (a)
∑F = m*a
F = m*a
42.6 = (9.58)*a
a = (42.6) / (9.58)
a = 4.45 m/s²
Kinematics Equation of the grocery cart
Because the grocery cart moves with uniformly accelerated movement we apply the following formula to calculate its final speed :
vf²=v₀²+2*a*d Formula (2)
Where:
d:displacement (m)
v₀: initial speed (m/s)
vf: final speed (m/s)
a: acceleration (m/s²)
Data:
v₀ = 0
a = 4.45 m/s²
d = 17.6 m
We replace data in the formula (2) :
vf²=v₀²+2*a*d
vf² = 0+2*(4.45)*(17.6)
vf² = 156.64
vf = 12.51 m/s