Question

How much work is required to increase the speed of a 8 kg cart from 4 m/s to 8 m/s?

Answer 1

Given the mass of the object, m= 8 kg.

Final speed of the object, v = 8 m/s

Initial speed of the object, u = 4 m/s

To find work done required to increase the speed from 4 m/s to 8 m/s

Work done = change in kinetic energy

Kinetic energy initially when speed is 4 m/s is given by

`KE._u=(1)/(2)mu^2`

Substituting the values, initial kinetic energy will be

`\begin{gathered} K\mathrm{}E._u=(1)/(2)*8*4^2 \\ =64\text{ J} \end{gathered}`

Similarly, final kinetic energy will be

`\begin{gathered} K\mathrm{}E._v=(1)/(2)mv^2 \\ =(1)/(2)*8*8^2 \\ =256\text{ J} \end{gathered}`

Work done will be

`\begin{gathered} W=K\mathrm{}E._v-K.E._u \\ =256-64 \\ =192\text{ J} \end{gathered}`

Thus, the required work done is 192 J.