Question

The mass of a body moving with a constant speed 36 km/h varies with time as m=2t+3√t +2 kg. What is the force associated with the body at t=2 s ? ​

Answer 1

Answer:

Given,

x=t

2

−4t+6

So, the change in velocity is:

dt

dx

=2t−4

Since velocity is changing,

At t=0,x

1

=6

At t=2,x

2

=2

So the magnitude of the distance traveled is:

6−2=4m

At t=3,x

3

=3

So distance traveled from t=2s to t=3s

x

3

−x

2

=3−2=1m

Thus the total distance is:

4+1=5m

Answer 2

Given: constant speed 36km/h, m=2t+3√t +2 kg

To find: force on body at t = 2s

Solution: We now that force acting on a body can be found with the formula

F= ma

where m is the mass of the body

a is acceleration of the body

It is given that mass is not constant here and it is changing with time.

also we know that

F= mdv/dt + vdm/dt

this is for non constant mass

here dv/dt will be zero because the body is moving with constant speed

therefore F= vdm/dt

now, m =2t+3√t +2 kg

dm/dt= 2+ 3/2× 1/√t + 0

putting value of t= 2sec in this equation we will get dm/dt at 2s

dm/dt = 2+ 3/2× 1/√2

F= vdm/dt

v= 36km/h = 10m/s

F= 10×(2+ 3/2× 1/√2)

F= 20+ 15/√2

Therefore, force associated with the body at t=2 s will be F= (20+ 15/√2)N