The kinetic energy of an object of mass, m moving with a velocity of 5 m s^–1 is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?

Given:
– Initial kinetic energy (KE₁) = 25 J
– Initial velocity (v₁) = 5 m/s
– Initial mass (m) is not specified, but it doesn’t affect the changes in kinetic energy due to changes in velocity.

Let’s solve for the kinetic energy when the velocity is doubled and tripled.

1. When velocity is doubled:
– Doubling the velocity means (v₂ = 2 x 5 m/s = 10 m/s).
– Using the kinetic energy formula (KE = 1/2 x m x v²), we can find (KE₂) when (v₂ = 10 m/s).

KE₂ = 1/2 x m x 10 m/s²
KE₂ = 1/2 x m x 100 J = 50 J

Therefore, when the velocity is doubled to (10 m/s), the kinetic energy becomes (50 J ).

2. When velocity is increased three times:
– Tripling the velocity means v₃ = 3 x 5 m/s = 15 m/s
– Using the same kinetic energy formula to find KE₃ when v₃ = 15 m/s.

KE₃ = 1/2 x m x 15 m/s²
KE₃ = 1/2 x m x 225 J = 112.5 J

Therefore, when the velocity is increased to 15 m/s, the kinetic energy becomes 112.5 J.

So, summarizing:
– When the velocity is doubled to (10 m/s), the kinetic energy becomes 50 J .
– When the velocity is increased three times to 15 m/s, the kinetic energy becomes 112.5 J.