Question

How much work must be done on a 5 kg snowboard to increase its speed from 2 m/s to 4 m/s

a) 30J
b) 15J
c) 40J
d) 22.5J

Answer 1

a) 30J

Step-by-step explanation:

use formula first find K.E with both speeds

K.E. = 1/2 m v2

and then

work done= change in kinetic energy

Answer 2

30 Joule of work is to be done.

Option: a

Step-by-step explanation:

Given, mass of snowboard = 5 Kg

Initial speed = 2 m/s, Final speed = 4 m/s, Work done = ΔE

Where, ΔE= change in kinetic energy

Solution:

`\text { Kinetic Energy (initial) }=(1)/(2) * \mathrm{mv}^(2)`

`\text { Kinetic Energy (initial) }=(1)/(2) * 5 \mathrm{Kg} *(2 \mathrm{m} / \mathrm{s})^(2)`

`(1)/(2) * 20 \mathrm{Kg} \cdot \mathrm{m}^(2) / \mathrm{s}^(2)` =
`10 \mathrm{Kg} \cdot \mathrm{m}^(2) / \mathrm{s}^(2)`

`\text { Kinetic Energy (final) }=(1)/(2) * m v^(2)`

`(1)/(2) * 5 \mathrm{Kg} *(4 \mathrm{m} / \mathrm{s})^(2)`

`(1)/(2) * 5 \mathrm{Kg} * 16 \mathrm{m}^(2) / \mathrm{s}^(2)`

`(1)/(2) * 80 \mathrm{Kg} \cdot \mathrm{m}^(2) / \mathrm{s}^(2)`

`40 \mathrm{Kg} \cdot \mathrm{m}^(2) / \mathrm{s}^(2)`

Work done = ΔE = Kinetic Energy (final) - Kinetic Energy (initial)

Work done = ΔE = 40 J - 10 J work done = ΔE = 30J