Question

The displacement x of a body of mass 1kg on horizontal smooth surface as a function of time t is given by x=t^4/4. The work done in first one second

Answer 1

See this photo answer is in this

Answer 2

Concept:

• Integration and calculus techniques
• Calculating the work done using force and displacement

Given:

• The mass of the body = 1 kg
• The displacement x = t^4/4 m

Find:

• The work done in the first one second by the object of mass 1kg

Solution:

x = t^4/4

v = dx/dt

v = d ( t^4/4)/dt

v = 4t^3/4

v = t^3

a = dv/dt

a = d(t^3)/dt

a = 3t^2

F = ma = 1 (3) (1)(1) = 3 N

X = 1/4 m

The work done = F.x = 3 *1/4 = 3/4 = 0.75 J

The work done in the first one second is 0.75 J

#SPJ2