Gabe M.

asked • 11/24/17# Finding Distance Using Mass and Force

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.

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## 2 Answers By Expert Tutors

Arturo O. answered • 11/24/17

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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)at

^{2}+ v_{0}t + x_{0}a = F/m = (12.0 N)/(17.5 kg) ≅ 0.6857 m/s

^{2}v

_{0}= 0 (started from rest)x

_{0}= 0 (set origin at the start point)⇒

x(t) = (1/2)at

^{2}= (1/2)(F/m)t^{2}x(3) = 0.5(0.6857)(3

^{2}) m ≅ 3.086 mMichael J. answered • 11/24/17

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Effective High School STEM Tutor & CUNY Math Peer Leader

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/s

^{2}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 = at

^{2}d = (0.866 m/s

^{2})(3 s^{2})Gabe M.

For the final part, you mean .686, right?

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11/24/17

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Arturo O.

11/24/17