Question

. Position of a particle of mass 1 kg varies
according to the equation
x(0) = (20 m/s)t + (30 m/s2)
(where t is in s). The force acting on the body at
time t= 1 s is​

Answer 1

Answer ⇒ Force = 60 N.

Explanation ⇒ There is an little mistake in the equation.

Correct equation will be,

x = 20t + 30t²

Now,

differentiating both sides with respect to time,

dx/dt = 20 + 30 × 2t

v = 20 + 60t

Again differentiating both sides w.r.t. time,

dv/dt = 0 + 60

∴ a = 60 m/s².

Thus,

 Force = mass × acceleration.

∴ Force = 1 × 60

∴ Force = 60 N.

We can see that acceleration now do not depends upon time, thus it will be same for every time t= 1, 2, etc.

Hope it helps.

Answer 2

Answer ⇒ Force = 60 N.

Explanation ⇒ There is an little mistake in the equation.

Correct equation will be,

x = 20t + 30t²

Now,

differentiating both sides with respect to time,

dx/dt = 20 + 30 × 2t

v = 20 + 60t

Again differentiating both sides w.r.t. time,

dv/dt = 0 + 60

∴ a = 60 m/s².

Thus,

 Force = mass × acceleration.

∴ Force = 1 × 60

∴ Force = 60 N.

We can see that acceleration now do not depends upon time, thus it will be same for every time t= 1, 2, etc.