Câu hỏi
The position of a particle is given by s(t)=4t^2-3t+1 where s is the position in meters and t is the time in seconds.What is the instantaneous rate of change of the position at t=2 seconds? None of these 10m/s 8m/s 13m/s 11m/s
Giải pháp
4.3
(184 Phiếu)
Giang
chuyên viên · Hướng dẫn 3 năm
Trả lời
The instantaneous rate of change of the position at
seconds is
.
Giải thích
## Step 1The instantaneous rate of change of the position of a particle at a given time is given by the derivative of the position function with respect to time. This is essentially the velocity of the particle at that specific time.## Step position function is given as \(s(t) = 4t^2 - 3t + 1\). To find the derivative of this function, we apply the power rule of differentiation, which states that the derivative of
is
.### **The derivative of \(s(t)\) is \(s'(t) = 8t - 3\)**## Step 3 the instantaneous rate of change at
seconds, we substitute
into the derivative function.### **The instantaneous rate of change at
is \(s'(2) = 8(2) - 3 = 16 - 3 = 13\)**