A shopper in a supermarket pushes a loaded
31 kg cart with a horizontal force of 12 N.
The acceleration of gravity is 9.81 m/s2 .
a) Disregarding friction, how far will the
cart move in 3.6 s, starting from rest?
Answer in units of m
F=ma
a=F/m
vf=at
A=9.81m/s^2
T=3.6s
Vi=0m/s
x=vit+.5at^2
x=(0*3.6)+(.5*9.81*3.6^2)
x=63.5688
To find the distance the cart will move, we can use the equation of motion:
d = 0.5 * a * t^2
Where:
d = distance traveled (unknown)
a = acceleration (which is given by the applied force divided by the mass of the cart)
t = time elapsed
First, we need to calculate the acceleration of the cart. The formula to find acceleration is:
a = F / m
Where:
F = force applied (12 N)
m = mass of the cart (31 kg)
Substituting the values into the equation, we get:
a = 12 N / 31 kg
Now, let's solve for acceleration:
a = 0.387 m/s^2
With the acceleration known, we can substitute it into the equation for distance:
d = 0.5 * 0.387 m/s^2 * (3.6 s)^2
Simplifying the equation, we get:
d = 0.5 * 0.387 m/s^2 * 12.96 s^2
Solving for d:
d = 0.5 * 0.387 * 167.616
d = 32.643 m
Therefore, the cart will move approximately 32.643 meters in 3.6 seconds, disregarding friction.