Final answer:
The magnitude of the applied force exerted on the 20 kg block that accelerates to 30 m/s from rest in 6 seconds over a frictionless surface is calculated using Newton's second law of motion to be 100 Newtons (N).
Step-by-step explanation:
The question involves calculating the magnitude of the applied force on a 20 kg block accelerating over a frictionless surface. To find the force, we use Newton's second law of motion, which states that Force (F) equals mass (m) times acceleration (a), or F = ma.
First, we need to calculate the acceleration of the block. Since it accelerates from rest to 30 m/s in 6 s, the acceleration (a) can be calculated using the formula a = (Δv) / t, where Δv is the change in velocity and t is the time taken. Therefore, a = (30 m/s - 0 m/s) / 6 s = 5 m/s².
Now, we can calculate the force using the mass of the block and the acceleration:
F = ma = (20 kg)(5 m/s²) = 100 N.
Thus, the magnitude of the applied force exerted on the block is 100 Newtons (N).