Question

A vehicle of mass 300kg is moving with a velocity of 27km/hr. It then increases its velocity to 36km/hr. Calculate the kinetic energy, the gain in the kinetic energy

Answer 1

Step-by-step explanation:

Formula:

$\frac{1}{2} m {v}^{2}$

m - mass

v - velocity

Kinetic Energy 1

$\frac{1}{2} \times 300 \times {27}^{2} \\ 150 \times 729 \\109350$

Kinetic Energy 2

$\frac{1}{2} \times 300 \times {36}^{2} \\150 \times 1296 \\ 194400$

Gain in Kinetic energy

$194400 - 109350 = 85050$

Answer 2

Solution :

As per the given data ,

• Mass of the vehicle (m) = 300 kg

• Initial velocity (u) = 27 km/hr = 27 x 5 / 18 = 7.5 m/s

• Final velocity (v) = 36 km / hr = 36 x 5 / 18 = 10 m/s

Kinetic energy is the energy possesed by an object due to it's motion .

Kinetic energy is given by ,

➜ KE = mv ² / 2

➢ Initial KE

➜ KE = mu² / 2

➜ KE = 300 x 7.5 x 7.5 / 2

➜ KE = 150 x 56.25

➜ KE = 8,437.25 J

➢ Final KE

➜ KE' = mv² / 2

➜ KE ' = 300 x 100 / 2

➜ KE' = 15,000 J

➢ Gain in KE

➜ KE net = KE' - KE

➜ KE net = 15,000 - 8,437.25

➜ KE net = 6562.75 J

The gain in KE is 6562.75 J