A body is moving initially at 4m/s. If it's impulse after accelerating at 5m/s\(^2\) for 2s is 60Kgms\(^{-1}\). What is its mass?

Answer Details

Impulse is defined as the change in momentum of a body. Mathematically, impulse \( J = \Delta p = m(v - u) \), where \( m \) is mass, \( v \) is final velocity, and \( u \) is initial velocity.

First, find the final velocity using the equation of motion:

\[ v = u + at = 4 + (5 \times 2) = 4 + 10 = 14 \text{ m/s} \]

Now substitute into the impulse equation:

\[ J = m(v - u) \]

\[ 60 = m(14 - 4) \]

\[ 60 = 10m \]

\[ m = \frac{60}{10} = 6 \text{ kg} \]

The mass of the body is 6 kg.

A common error is to confuse impulse with final momentum (\( mv \)) rather than the change in momentum (\( m \Delta v \)). Impulse equals \( F \times t \) or equivalently \( m(v - u) \); both routes give the same result here since \( F \times t = ma \times t = m \times 5 \times 2 = 10m \).