Question

A net force with magnitude (5.00 N/m2)x2 and directed at a constant angle of 31.0o with the +x-axis acts on an object of mass 0.250 kg as the object moves parallel to the x-axis. How fast is the object moving at x = 1.50 m if it has a speed of 4.00 m/s at x = 1.00 m?

Answer 1

A net force with magnitude (5.00 N/m2)x2 and directed at a constant angle of 31.0o with the +x-axis acts on an object of mass 0.250 kg as the object moves parallel to the x-axis. How fast is the object moving at x = 1.50 m if it has a speed of 4.00 m/s at x = 1.00 m?

The horizontal component of the force is the component that will cause the object to accelerate, and it has a magnitude of

$$F _ {x} = F \cos (3 1 {}^ {\circ}) = 0. 8 6 F$$

Using second Newton's law:

$$F _ {x} = m a \rightarrow a = \frac {0 . 8 6 F}{m} = \frac {0 . 8 6 * 5 N}{0 . 2 5 k g} = 1 7. 2 m / s ^ {2}$$

At time $t$ object's position is:

$$x = x _ {0} + \frac {v ^ {2} - v _ {0} ^ {2}}{2 a}$$

Assuming that $x = 1m$ is a starting point for object with $v_{0} = 4m / s$ :

$$v ^ {2} = v _ {0} ^ {2} + 2 (x - x _ {0}) a$$ $$v = \sqrt {v _ {0} ^ {2} + 2 (x - x _ {0}) a}$$ $$v = \sqrt {(4 m / s) ^ {2} + 2 * (1 . 5 m - 1 m) * 1 7 . 2 m / s ^ {2}} = 5. 7 6 m / s$$

Answer: $v = 5.76 \, \text{m/s}$