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.
v= 46.2
D= 66 ft
To determine the final velocity and the distance traveled by the 10-lb block, we will use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
Given:
- Mass of the block (m) = 10 lb
- Initial velocity of the block (v0) = 10 ft/s
- Force acting on the block (F) = 2.5t, where t is in seconds
- Time duration (t) = 3 seconds
Step 1: Calculate the acceleration
We can find the acceleration by dividing the force by the mass:
a = F / m
= (2.5t) / 10
Step 2: Calculate the final velocity
The final velocity can be found using the kinematic equation:
vf = v0 + at
= 10 + (2.5t / 10) * 3
Step 3: Calculate the distance traveled
The distance traveled can be determined using another kinematic equation:
d = v0t + (1/2)at^2
= 10 * 3 + (1/2) * (2.5t / 10) * 3^2
Now, we can substitute the given values into these equations to find the final velocity and distance traveled at t = 3 seconds.