Question

A particle moves in a straight line and has acceleration given by a(t)=−t+1 m/s². Its initial velocity is v(0)=4 m/s and its initial displacement is s(0)=7 m. Find its position function s(t).

Answer 1

s(t) = (-t^3)/3 + (t^2)/2 + 4t + 7

Step-by-step explanation:

a = -t +1

to find the equation for velocity we need to integrate the acceleration equation,

v = (-t^2)/2 + t + c

c is an arbitrary constant

as it is given v(0) = 4 m/s

4 = 0 + 0 + c

c = 4

now let's integrate again to find the displacement equation,

s = (-t^3)/3 + (t^2)/2 + 4t + c1

c1 is an arbitrary constant

given s(0) = 7m

7 = 0 + 0 + 0 + c1

c1 = 7

so the final answer is,

s(t) = (-t^3)/3 + (t^2)/2 + 4t + 7