An object has a constant acceleration of 40 ft/sec^2, an initial velocity of −20 ft/sec, and an initial position of 10 ft. Find the position function, s(t), describing the motion of the object.
To find the position function, s(t), describing the motion of the object, we can use the kinematic equation which relates position, velocity, acceleration, and time.
The kinematic equation is given by:
s(t) = s0 + v0t + (1/2)at^2
Where:
s(t) is the position at time t
s0 is the initial position
v0 is the initial velocity
a is the acceleration
t is the time elapsed
Given values:
s0 = 10 ft (initial position)
v0 = -20 ft/sec (initial velocity)
a = 40 ft/sec^2 (constant acceleration)
Substituting these values into the kinematic equation, we have:
s(t) = 10 + (-20)t + (1/2)(40)t^2
Simplifying further:
s(t) = 10 - 20t + 20t^2
Therefore, the position function, s(t), describing the motion of the object is:
s(t) = 10 - 20t + 20t^2