The 10-lb has an initial velocity of 10ft/s on the smooth plane. If a force F=(2.5t), where t is in seconds, acts on the block for 3s, determine the final velocity of the block and the distance the block travels during this time.

Answer 1

Is the F = 2.5t force in pounds? I will assume so.

The mass of the object being accelerated is W/g = 0.3106 slugs.
The final velocity after 3 seconds is the impulse divided by the mass, or
Integral (0 to 3)of F*dt/0.3106= 1.25*3^2/0.3106 = 36.2 ft/s.

Distance travelled = Integral (0 to 3) of (acceleration)*dt
acceleration = F/m = 2.5 t/0.3106 = 8.049t ft/s^2. I will leave that part up to you.

The average velocity is not half the maximum (final velocity) in this case, since the object acceleration increeases.