Finding Distance Using Mass and Force

Question

In a grocery store, you push a 17.5 kg shopping cart with a force of 12.0 N. If the cart starts at rest, how far does it move in 3.00 s?

 

How would I solve this? It's for an online class I'm taking, and the notes say literally nothing about this. Would I use F=MA?

 

Thanks in advance.

Answer 1

If the net applied force is a constant F = 12.0 N (see my comment) throughout the entire travel distance of x, then you have constant acceleration motion, and

 

x(t) = (1/2)at² + v₀t + x₀

 

a = F/m = (12.0 N)/(17.5 kg) ≅ 0.6857 m/s²

v₀ = 0 (started from rest)

x₀ = 0 (set origin at the start point)

 

⇒

 

x(t) = (1/2)at² = (1/2)(F/m)t²

 

x(3) = 0.5(0.6857)(3²) m ≅ 3.086 m

Answer 2

You would use F = ma.  However, you want the distance.  So you have to solve for a first. Then use the formula for velocity and distance to get your distance.

 

a = F / m

a = 12 / 17.5

a = 0.686 m/s²

 

Then, use the formula

 

d = vt

 

 

We can write v in terms of a and t,

 

a = v/t

 

v = at

 

 

Then your formula for distance, substituting in the value of v is

 

d = (at)t

 

d = at²

 

d = (0.866 m/s²)(3 s²)