What is the Velocity of a Block Pushed by a Linear Force Function?

[Innuendo]

Homework Statement

A force of F(t) = t is pushing a block of 5kg mass with no friction. What is the velocity after 10 seconds?

Homework Equations

F=ma

The Attempt at a Solution

F(10) = 10 N

a = F/m = 10/5 = 2 m/s^2

a = dv/dt

v(t) = 2t

v(10) = 20 m/s


I've calculated the acceleration by plugging in the time into F(t) and integrated the acceleration to find v(t). But when I plug in the time again into v(t), is that the right step?

 

[ehild]

The acceleration is not constant, 2m/s². If the force depends on t so does the acceleration, as it is a=F/m.

ehild

 

[Innuendo]

So I should carry the t in the force and set a(t) = F(t) / m ?
a(t) = t / 5

v(t) = t^2 / 10
v(10) = 10 m/s?

 

[ehild]

Supposing that the block had 0 velocity at the beginning, your result is correct.

ehild

 

[Innuendo]

ahh thank you