To solve this problem, let's first convert the time from minutes to seconds:
10 minutes = 10 × 60 seconds = 600 seconds
Given: Mass of the tractor (m) = 1500 kg Initial velocity (u) = 0 m/s (since it starts from rest) Final velocity (v) = 20 m/s Time taken (t) = 600 seconds
We can use the equation of motion:
v = u + at
Where: v = final velocity u = initial velocity a = acceleration t = time taken
Substituting the known values:
20 m/s = 0 m/s + a × 600 s
Simplifying the equation:
20 m/s = 600 a
Now, we can solve for the acceleration (a):
a = 20 m/s / 600 s a ≈ 0.0333 m/s²
So, the acceleration of the tractor is approximately 0.0333 m/s².
To find the distance covered (s), we can use another equation of motion:
s = ut + (1/2)at²
Where: s = distance covered
Substituting the values:
s = 0 m/s × 600 s + (1/2) × 0.0333 m/s² × (600 s)²
Simplifying the equation:
s = 0 + 0.5 × 0.0333 m/s² × 360,000 s²
s ≈ 6,000 m
So, the distance covered by the tractor is approximately 6,000 meters.
To calculate the net force (F) acting on the tractor, we can use Newton's second law of motion:
F = ma
Where: m = mass of the tractor a = acceleration
Substituting the values:
F = 1500 kg × 0.0333 m/s²
F ≈ 49.95 N
So, the net force acting on the tractor as it accelerates is approximately 49.95 Newtons.