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

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A block with a mass of 5 kg is pushed by a linear force function F(t) = t, resulting in a force of 10 N after 10 seconds. The acceleration is calculated as a = F/m = 2 m/s², but since the force varies with time, the acceleration also changes. The correct approach involves setting a(t) = F(t) / m, leading to a(t) = t / 5. Integrating this gives the velocity function v(t) = t² / 10, resulting in a velocity of 10 m/s after 10 seconds, assuming the block starts from rest. The calculations confirm the importance of considering the time-dependent nature of the force and acceleration.
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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?
 
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The acceleration is not constant, 2m/s2. If the force depends on t so does the acceleration, as it is a=F/m.

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

ehild
 
ahh thank you
 

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