Question

A force of 150 N acts on a 0.20-kg cart so as to accelerate it along an air track. The track and force are horizontal and in line with each other. How fast is the cart going after acceleration from rest through 30 cm, if friction is negligible?

Answer 1

*****VERY VERY IMPORTANT - I SUSPECT THE VALUE OF FORCE GIVEN IN THE QUESTION. 150 N is too high, because it will give an acceleration of too high magnitude. I think the force should be 1.50 N (please check this). If it is 150 N, no problem use the same method as below,

Anyway, here is the method which we can use to solve for the velocity after 30 cm.

we can solve using two methods

using work energy theorem

W = 1/2mv²

F*d = 1/2mv²

v = sqrt (2Fd / m)

v = sqrt (2*1.5*0.3 / 0.2)

v = 2.12 m/s

Using newton's law and kinematics

F = ma

a = F/m

a = 1.50 / 0.20

a = 7.50 m/s²

Now, use the kinematics

v² = u² + 2ad

as it starts from rest, u = 0

v = sqrt (2ad)

v = sqrt (2*7.50*0.3)

v = 2.12 m/s

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If the force is 150 N

then

v = 21.21 m/s (method is same as used above)