3 questions about The resultant force equation

1. A car with a mass of 5 tonnes moves from rest in 50 seconds, reaching a speed of 72 km/hour. The force on the car is…

__Known:__

Mass (m) = 5 tons = 5000 kg

Initial speed (vo) = 0

Final speed (vt) = 72 km/h = 20 m/s

Time interval (t) = 50 seconds

__Wanted:__ Force (F)

__Solution:__

Calculate the acceleration using the Non Uniform Linear Motion formula:

v_{t} = v_{o} + a t

20 = 0 + a (50)

20 = 50 a

a = 20 / 50 = 0,4 m/s^{2}

Calculate the resultant force using Newton’s second law formula:

ΣF = m a

F = (5000)(0,4) = 2000 Newton

2. A car has a mass of 1 ton, for 4 seconds its speed increases uniformly from 10 m/s to 18 m/s. Determine the magnitude of the force that accelerates the car.

__Known:__

The mass of the car (m) = 1 ton = 1000 kg

Time interval (t) = 4 seconds

Initial velocity (v_{o}) = 10 m/s

Final velocity (v_{t}) = 18 m/s

__Wanted:__ Force (F)

__Solution:__

Calculate the acceleration using the Non Uniform Linear Motion formula:

v_{t} = v_{o} + a t

18 = 10 + a (4)

18 – 10 = a (4)

8 = 4 a

a = 8 / 4 = 2 m/s^{2}

Calculate the resultant force using Newton’s second law formula:

ΣF = m a

F = (1000)(2) = 2000 Newton

3. The two force vectors are perpendicular to each other which results in a resultant of 10 N. If one of the force vectors is 6 N , determine the magnitude of the other force vector.

__Known:__

Resultant force (F) = 10 N

Force 1 (F_{1}) = 6 N

__Wanted:__ Force 2 (F_{2})

__Solution:__

F_{2} = 10 – 6 = 4 Newton