A particle of mass 10 kg is acted on by a resultant force, F newtons. If the position vector of the particle is given by r = 6ti + (4t + 8t2)j, then F is equal toĻ
To find the force acting on the particle, we need to determine its acceleration. We can find the acceleration by taking the second derivative of the position vector with respect to time.
Given: r = 6ti + (4t + 8t^2)j
First, we differentiate r with respect to time to find the velocity vector v:
v = dr/dt = 6i + (4 + 16t)j
Next, we differentiate v with respect to time to find the acceleration vector a:
a = dv/dt = d²r/dt² = 0i + 16j
Now we know that the acceleration vector is constant and given by a = 0i + 16j.
Since force (F) is defined as mass (m) multiplied by acceleration (a), we can find the force acting on the particle by multiplying the mass (10 kg) by the acceleration vector (0i + 16j).
F = m * a = 10 kg * (0i + 16j) = 0i + 160j
Therefore, the force (F) acting on the particle is equal to 0i + 160j.