Question

A 900 kg compact car is moving at a certain speed if its kinetic energy is 320000 Joule find the velocity at which the car is travelling

Answer 1

mass = m = 900kg

K.E = 320000J = 320×10³J

velocity = v = ?
_______________

K.E = mv²/2

2×K.E = mv²

2×320×10³ = 9×10²×v²

640×10³/9×10² = v²

640×10^3-2/9 = v²

640×10¹/9 = v²

64×10²/9 = v²

√64×10²/9 = v

8×10/3 = v

80/3 = v

26.67m/s = v
______________________
so car's velocity is 26.67m/s

Answer 2

Given,

1. The mass of the compact car(m) = 900 kg
2. Kinetic Energy of the car moving at a certain speed = 320000 J

To find,

The velocity at which the car is traveling.

Solution,

When a mass is moving at a particular speed with having given kinetic energy, it will have a certain velocity.

Let the velocity of the moving car be v.

We can express the kinetic energy as,

Kinetic Energy = 320000 J = 32 × 10⁴ J

Now, we know the formula for finding the kinetic energy of a moving object,

Kinetic Energy (KE) = $\frac{1}{2}$mv²

⇒ 32 × 10⁴ = $\frac{1}{2}$ × 900 × v²

⇒ v² = 32 × 10⁴ × 2 × $\frac{1}{900}$

⇒ v² = $\frac{6400}{9}$

⇒ v = $\sqrt{\frac{6400}{9}}$ = $\frac{80}{3}$ = 26.67 ms⁻¹

Hence, the velocity at which the car was moving is 26.67 ms⁻¹.