Question #113306

A 2.0 kg object is moving across a table at constant speed of 2.0 m/s against a force of friction of 6.0 N. The applied force is suddenly increased by 1.0 N. How fast will the object be moving after 3.0 s?

Expert's answer

**Explanation**

- First, the object was moving at a constant velocity meaning that no acceleration along the moving direction ; hence applied force & the frictional force are equal in magnitude.
- After the sudden increment of the applied force,a net unbalanced force of
**(7N-6N =) 1N**is being applied on the object resulting an acceleration & increasing its velocity thereafter. - Soon after the motion turns to a linear motion under an acceleration with an initial velocity of 2ms
^{-1}.

**Notations**

- Refer to the sketch attached.

**Calculations**

- Apply F = ma to the object along the moving direction

"\\qquad\\qquad\n\\begin{aligned}\n\\small 1N &= \\small 2kg \\times a_1\\\\\n\\small a_1 &= \\small 0.5ms^{-2}\n\\end{aligned}"

- Finding the velocity after 3s can be found by linear motion just started under the new acceleration.

"\\qquad\\qquad\n\\begin{aligned}\n v &= u+at\\\\\nv &= \\small 2ms^{-1} + 0.5ms^{-2} \\times 3s \\\\\n v &= \\small \\bold{3.5ms^{-1}}\n\\end{aligned}"

**Good Luck**

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