Question

Calculate the force required to impart a car a velocity of 20 m/s in 8 seconds. Given that

the mass of the car is 1200 kg.​

Answer 1

3000 N is the required answer

GIVEN:

• Mass of the car, m = 1200 kg
• Velocity, v = 20 m/s (final velocity)
• Time, t = 8 seconds
• Consider the car to be at rest initially. So initial velocity, u = 0

TO FIND:

Force, f

FORMULAE:

• According to first equation of motion, v = u + at

• According to Newton's second law, f = ma

SOLUTION:

STEP 1: To find acceleration

v = u + at

20 = 0 + (a×8)

20 = 8a

a = 20/8

a = 10/4

a = 5/2

a = 2.5 m/s²

Acceleration of the car is 2.5 m/s²

STEP 2: To find force

f = ma

f = 1200 × 2.5

f = 1200 × (5/2)

f = 600 × 5

f = 3000 N

ANSWER:

Force imparted to the car is 3000 N.

DIRECT FORMULA:

f = m(v-u)/t

OTHER METHOD:

• f = dp /dt

• p = mv

Here p is the momentum.

p = 1200 × 20

p = 24000 kg m/s

f = dp/dt

f = 24000 / 8

f = 3000 N