An object moves according to the law s = t2 + 5t - 8. what is the exact rate of change of s with respect to t when t = 1.5 seconds?

Replace t with 1.5 seconds and solve for s:

s = 1.5^2 + 5 (1.5) - 8

s = 2.25+7.5-8

s = 9.75 - 8

s = 1.75

Rate of change is S/t

Rate of change = 1.75 / 1.5

Rate of change of s = 1.17

ds/dt = 8 when t = 1.5

Step-by-step explanation:

s = t^2 + 5t - 8

We want to find ds/dt

ds/dt = 2t + 5

evaluated when t=1.5

ds/dt = 2 (1.5) + 5

ds/dt = 3+5

ds/dt = 8 when t = 1.5