Question

The velocity of particle is given as v = 3t2 + t-1/2 calculate the net force acting on the
body at time t = 2s, if mass of the body is 5 kgs.
A) 156.75 N
B) 125.25 N
C) 186.25 N
D) 175.25 N
OA​

Answer 1

Answer :

Required force = 65 N

Solution :

→ Given :

• Velocity , v = 3t² + t - ½

• Mass of body , m = 5kg

→ To find :

• Force , F at t = 2 s

Now ,

We know that , the instantaneous acceleration of a body is given as :

a = dv/dt where v is the velocity .

Thus ,

=> a = dv/dt

=> a = d(3t² + t - ½)/dt

=> a = d(3t²)/dt + dt/dt - d(½)/dt

=> a = 3dt²/dt + dt/dt - d(½)/dt

=> a = 3×2t + 1 - 0

=> a = 6t + 1

Now ,

The acceleration of the body at t = 2 s will be ;

=> a = 6×2 + 1

=> a = 12 + 1

=> a = 13

Now ,

The force acting on the body at t = 2 s will be ;

=> F = ma

=> F = 5 × 13

=> F = 65 N

Hence ,

Required force = 65 N