Answer:
[tex]299 m/s^2[/tex]
Explanation:
When a spring is compressed, the force exerted by the spring is given by:
[tex]F=kx[/tex]
where
k is the spring constant
x is the compression of the spring
In this problem we have:
k = 52 N/m is the spring constant
x = 43 cm = 0.43 m is the compression
Therefore, the force exerted by the spring on the dart is
[tex]F=(52)(0.43)=22.4 N[/tex]
Now we can apply Newton' second law of motion to calculate the acceleration of the dart:
[tex]F=ma[/tex]
where
F = 22.4 N is the force exerted on the dart by the spring
m = 75 g = 0.075 kg is the mass of the dart
a is its acceleration
Solving for a,
[tex]a=\frac{F}{m}=\frac{22.4}{0.075}=299 m/s^2[/tex]
