8. If a constant force acts on a body initially kept at rest. The distance travelled by the body in time
t is proportional to :
(a)t
(b) t²
(c) 13
(d) 1/1
Answers
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Assuming that you mean that the body was at rest at the point in time that the force was applied, and not kept at rest initially during force application, and that the applied force is the only force acting ( i.e. frictionless environment ), then the body will experience an acceleration given by Newton’s Third Law, which is mathematically expressed
as F = ma, as being the acceleration, F the force, and m the mass. The acceleration the body experiences is therefore directly proportional to the force size, and inversely proportional to it’s mass.
Distance traveled in time t can be calculated from one of the 5 equations derived for uniformly accelerated rectilinear/straight line motion. 5 variables, viz initial velocity, final velocity, acceleration a, time of acceleration t, and distance traveled d, require 5 equations.
Here, the appropriate one is d = v ( initial ) times t +1/2 times a times t squared.
Since v(initial) = 0, the first right-hand term becomes zero, so the distance traveled is 1/2 a times t squared.
Distance is directly proportional to the square of the time under acceleration, and directly proportional to the acceleration, which, in turn, is directly proportional to the force, and inversely proportional to the bodies mass.