Rate of Change

Question

An object is moving in a straight line from a fixed point. The displacement s(in meters) is given by s=-2t^2+28t+45, t is greater than or equal to 0, where t is in seconds. 

 

1. Describe the direction of the motion at, t=3s, t=7s, and t=9s

Answer 1

s(0) = 45

 

s(3) = -2*3^2 + 28 * 3 + 45 = -2 * 9 + 28 *3 + 45 = -18 + 84 + 45 = 111

 

s(7) = -2 * 7^2 + 28*7 + 45 = -98 + 196 + 45 = 143

 

s(9) = -2 * 9^2 + 28*9 + 45 = -162 + 252 + 45 = 135

 

Wherever the initial point is, at 3 seconds, the object moved away from it.

Then at 7 seconds, the object moves farther away because the displacement increased.

Then at 9 seconds, the object moved closer to the initial point because the displacement decreased.

 

As mentioned in the previous problem, the displacement is the largest at 7 seconds,

because the derivative of the displacement function is -4t + 28, which when set

equal to zero, produces a maximum of 7 seconds when solved for t.