Find the force needed to accelerate a mass of 40kg from velocity ⃗ ( ̂ ̂
̂) to ⃗ ( ̂ ̂ ̂) in 10s
First, calculate the acceleration required to change the velocity from ⃗ ( ̂ ̂ ̂) to ⃗ ( ̂ ̂) in 10 seconds:
Velocity change = final velocity - initial velocity
Velocity change = ⃗ ( ̂ ̂) - ⃗ ( ̂ ̂ ̂)
Velocity change = ⃗ ( ̂ ̂ - ̂ ̂ ̂)
Velocity change = ⃗ ( - ̂)
Velocity change = -⃗ ( ̂)
Acceleration = Velocity change / Time taken
Acceleration = -⃗ ( ̂) / 10 s
Acceleration = -0.1( ̂) m/s^2
Next, calculate the force needed to accelerate a mass of 40 kg at this acceleration rate:
Force = mass x acceleration
Force = 40 kg x -0.1( ̂) m/s^2
Force = -4( ̂) N
Therefore, the force needed to accelerate a 40 kg mass from velocity ⃗ ( ̂ ̂ ̂) to ⃗ ( ̂ ̂) in 10 seconds is -4( ̂) N.