Question

A car of mass 1000 kg gets accelerated from rest to 8 m/s in 4 seconds. Find it’s


i) Initial momentum

ii) Final momentum


iii) Acceleration

iv) Magnitude of the force exerted by its engine.​

Answer 1

Answer:

(i) 0 (ii) 8000 (III) 2 (iv) 2000

Given

Mass of the car = m = 1000 kg.

u (initial velocity) = 0 m/s

v = 8 m/s

Formulas

Momentum = P = mass × velocity

F = ma where a = $\dfrac{v\:-\:u}{t}$

Calculations

(I) Initial momentum = mass × initial velocity = 1000 × 0 = 0.

Initial momentum is 0 kg m/s.

(ii) Final momentum = Mass × final velocity = 1000 × 8 = 8000

Final momentum is 8000 kg m/s.

(III) acceleration = $\dfrac{v\:-\:u}{t}$

= $\dfrac{8\:-\:0}{4}$

= 2

Acceleration of the car is 2 m/s².

(iv) Force = mass × acceleration = 1000 × 2 = 2000

Force on the car is 2000 N.

Answer 2

Explanation:

Given; mass is 1000 kg, initial velocity is 0 m/s, final velocity is 8 m/s and time is 4 sec.

To find: Initial momentum, final momentum, acceleration and magnitude of the force exerted by its engine.

a) Initial momentum = Mass × Initial velocity

= 1000 × 0

= 0 kg m/s

b) Final momentum = Mass × Final velocity

= 1000 × 8

= 8000 kg m/s

c) Using first equation of motion,

v = u + at

8 = 0 + a(4)

8 = 4a

2 = a

Acceleration is 2 m/s².

d) Force = Mass × Acceleration

Force = 1000 × 2

Force = 2000 N