Question

Find expressions for the force needed to bring an object of mass m from rest to speed v in time t. express your answer in terms of the variables m, v, and t.

Answer 1

Good morning.

We have that:

$\mathsf{V = a\cdot t}$ , since we have rest in the inicial time.

The acceleration can be found with Newton's Law:

$\mathsf{F = m\cdot a\iff a = \dfrac{F}{m}}$

Now we put the acceleratin in the velocity equation:

$\mathsf{V = \dfrac{F}{m} \cdot t}$

We want the force, so, let's isolate F:

$\mathsf{V\cdot m = F\cdot t}\\ \\ \\ \boxed{\mathsf{F = \dfrac{V\cdot m}{t}}}$