Question

An object is covering distance in direct proportion to t3,where t is time elapsed a)what conclusion might you draw about the acceleration?is its constant or increasing or decreasing or zero with time. b)what might you conclude about the force acting on the object?is it constant or increasing or decreasing or zero with time.

Answer 1

since distance is directly proportional to cube of time

(a) d=kt³. (k is constant of proportionality,k=1 in SI)

d=t³

differentiation of aboub equation is

v=2t²

one step differentiate again then we get

a=4t

since accelration is increasing with increase in fourth second of time.

(b)since force is given by

f=ma

here mass of body remain constant

f=a

since force is directly proportional to accelration, as accelration increase force increase with fourth second of time

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