A 1.5 N force acts on a .20 kg cart so as to accelerate it along a frictionless track. If it is accelerated from rest, how fast is it going after .3m?
The answer given is 2.12 m/s but I am not sure how to get to that.
F = ma
1.5 = .2 a
7.5 = a
s = 1/2 at^2
.3 = 3.75 t^2
t = .2828
v = at
= 7.5*.2828
= 2.12
Of course, by combining all those formulas, you could have just used
v = sqrt(2sF/m)
To solve this problem, you can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. The equation for Newton's second law is:
F = m * a
Where:
F is the force applied to the cart (1.5 N in this case)
m is the mass of the cart (0.20 kg in this case)
a is the acceleration of the cart
You are given the force and the mass of the cart, so you need to find the acceleration first. Rearrange the equation to solve for acceleration:
a = F / m
a = 1.5 N / 0.20 kg
a = 7.5 m/s²
Now that we have the acceleration, we can use kinematic equations to find the final velocity (v) of the cart. In this case, we know the initial velocity is zero (as the cart starts from rest). We can use the following equation:
v² = u² + 2as
Where:
v is the final velocity
u is the initial velocity (zero in this case)
a is the acceleration (7.5 m/s² in this case)
s is the distance traveled (.3m in this case)
Rearrange the equation to solve for the final velocity:
v² = 0 + 2 * 7.5 m/s² * .3m
v² = 2.25 m²/s²
v = √2.25 m/s
v ≈ 1.5 m/s
So, the cart is going approximately 1.5 m/s after traveling 0.3m. The answer you provided (2.12 m/s) seems to be incorrect based on the calculations of the provided data.