A particle moves along an x axis, being propelled by a variable force directed along that axis. Its position is given by role="math" localid="1657014461331" , with x in meters and t in seconds. The factor c is a constant. At the force on the particle has a magnitude of and is in the negative direction of the axis. What is c?
The value of constant c is
The acceleration of the object is equal to the time rate of change of velocity. The acceleration can be found by differentiating the velocity vector with respect to time or differentiating the displacement vector twice with respect to time.
As we are given the function for the position of a particle if we differentiate that for time, we will get twice the acceleration. As we have got the value of force at a particular time, using Newton’s 2nd law, we can find the value for c.
The force on a body due to Newton’s second law, (i)
Here, is net force, is mass of the object, and is the acceleration.
The acceleration of a body in motion, (ii)
Taking the derivative of the given position equation with respect to time, we get the velocity as follows:
A 80 kg man drops to a concrete patio from a window 0.50 m above the patio. He neglects to bend his knees on landing, taking 2.0 cm to stop. (a) What is his average acceleration from when his feet first touch the patio to when he stops? (b) What is the magnitude of the average stopping force exerted on him by the patio?
Two horizontal forces,
pull a banana split across a frictionlesslunch counter. Without using acalculator, determine which of thevectors in the free-body diagram ofFig. 5-20 best represent (a) and(b) . What is the net-force componentalong (c) the x axis and (d) the yaxis? Into which quadrants do (e) thenet-force vector and (f) the split’s accelerationvector point?
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