Question

A force F acts on a particle of mass 1 kg according to F(t)= 2t , where t is in seconds. If the particle starts from rest, then its speed after 5 sec is

Answer 1

We know that F = m a
where,
F = Force
m = mass of an object
a = acceleration of that object

"By integrating from t=0 to t=5 on both side in given equation, we get answer. Given that initial velocity is zero"

Answer 2

Given:

Mass of the particle, m = 1 kg

Force on the particle is given by,

F(t) = 2t

where t is time in seconds.

Let acceleration and velocity of the particle be a and v respectively.

Find:

Its speed after 5 seconds.

Solution:

The given force is,

F(t) = 2t      or

F = 2t

But F = ma = mass x acceleration

Now, F = ma = 2t

ma = 2t

a = 2t/m

But a = dv/dt

∴ dv/dt = 2t/m

dv = (2t/m)dt

Integrating both sides, we get

∫ dv =  ∫ (2t/m)dt

v = (2/m)  ∫ t dt

v = (2/m) (t²/2) + c

v = (2/m) × (t²/2) + c

v = t²/m + c                   --------------- (i)

As body starts from rest, v = 0 at t = 0.

∴ 0 = 0²/m + c

0 = 0 + c

c = 0

Putting the value of c in (i), we get

v = t²/m

So, after five seconds, t = 5 s

∴ v = 5²/1

v = 25 m/s

Hence, the speed of the particle after 5 seconds is 25 m/s.

#SPJ2