A shopper in a supermarket pushes a loaded

37 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 3.8 s, starting from rest?
Answer in units of m

gravity has noting to do with it if no friction.

a = F/m = 12/37

d = (1/2)(12/37)(3.8)^2

2.341

To find the distance the cart will move in 3.8 seconds, we need to use the kinematic equation:

\[d = \frac{1}{2} \cdot a \cdot t^2\]

Where:
d = distance
a = acceleration
t = time

In this case, the acceleration (a) is not given directly, but we can calculate it by using Newton's second law: \(F = m \cdot a\), where F is the applied force and m is the mass of the cart.

Given:
Force (F) = 12 N
Mass (m) = 37 kg
Time (t) = 3.8 s

First, let's calculate the acceleration:
\[F = m \cdot a\]
\[12 \, N = 37 \, kg \cdot a\]
\[a = \frac{12 \, N}{37 \, kg}\]

Now we can substitute the value of acceleration into the kinematic equation to find the distance:
\[d = \frac{1}{2} \cdot a \cdot t^2\]
\[d = \frac{1}{2} \cdot \left(\frac{12 \, N}{37 \, kg}\right) \cdot (3.8 \, s)^2\]

Calculating this expression will give us the distance moved by the cart in 3.8 seconds, starting from rest.