Question

(a) State and explain Newton's second law of motion.
(b) A 1000 kg vehicle moving with a speed of 20 m/s is brought to rest in a distance of 50 metres :
(i) Find the acceleration
(ii) Calculate the unbalanced force acting on the vehicle.

Answer 1

(a) Newton’s Second law of motion states that the force ‘F’ acting on a body of mass ‘m’ producing acceleration ‘a’ is equal to the product of the mass and acceleration of the body. That is, F = ma
It can be derived from the concept of momentum.
Suppose a body of mass ‘m’ has initial velocity ‘u’ and after time ‘t’ its velocity becomes ‘v’. The initial momentum is, P_i = mu
The final momentum is P_f = mv
The change in momentum with respect to time ‘t’ is
= (mv − mu)/t = m (v − u)/t = F …….(1)
We know, acceleration, a = (v − u)/t
So, (1) implies,
F = m(v − u)/t = ma
Which is Newton’s Second law of motion.

(b) (i) Final velocity, v = 0 (because the car is brought to rest)
Distance covered, s = 50 m
So, Force = mass × acceleration
But we do not know the value of a.
Making use of the third equation of motion we get,
v² − u² = 2as
⇒ 0 − 20² = 2 × a × 50
⇒ −400 = 100a
⇒ a = −4
The acceleration = −4 m/s²

(ii) Force = mass × acceleration
Mass = 1000 kg
Force = 1000 × (−4)
= − 4000 N
Unbalanced force acting on the vehicle is −4000 N.