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Question

(please show how you got answer)an object has a constant acceleration of (75)feet per second square, an initial velocity of (17) feet per second , and an initial position of (10) feet.Find the position function describing the motion of this object.

Answer 1

Acceleration is rate of change of speed. If we call speed v, then dv/dt=a, where a is the constant acceleration. We can write dv=adt and integrate both sides: v=u+at where u is an initial speed. Speed is the rate of change of distance, so if distance is x then dx/dt=v=u+at. We can write this dx=(u+at)dt and integrate both sides: x=ut+(at^2)/2+s, where s is an initial distance or position. Now we are given a=75, u=17 and s=10. The units are feet and seconds. Therefore, x=17t+75(t^2)/2+10 or x=10+17t+37.5t^2. This is the position function, where x is in feet and t is in seconds.