Question

b) a bug is moving back and forth on a straight path. the velocity of the bug is given by ( v(t)=t^{2}-3 t ). find the average acceleration of the bug over the interval ( 1,4 ).

Explanation:

Step1: Recall the formula for average acceleration

The formula for average acceleration \(a_{avg}=\frac{v(t_2)-v(t_1)}{t_2 - t_1}\), where \(t_1 = 1\) and \(t_2=4\)

Step2: Find \(v(1)\) and \(v(4)\)

Given \(v(t)=t^{2}-3t\)
For \(t = 1\): \(v(1)=1^{2}-3\times1=1 - 3=-2\)
For \(t = 4\): \(v(4)=4^{2}-3\times4=16 - 12 = 4\)

Step3: Calculate the average acceleration

Substitute into the formula: \(a_{avg}=\frac{v(4)-v(1)}{4 - 1}=\frac{4-(-2)}{3}=\frac{4 + 2}{3}=\frac{6}{3}=2\)

Answer:

\(2\)