Question

A mouse runs along a baseboard in your house. The mouse's position as a function of time is given by x(t)=pt2+qt, with p = 0. 40 m/s2 and q = -1. 10 m/s.

Answer 1

The  average speed between t = 1.0 s and t = 4.0 s will be 2.1+0.3 which is 2.4m/s

Velocity function

Given the equation for the position of the mouse expressed as:

$x(t)=pt^2+qt$

The velocity of the particle is expressed as:

$v(t)=2pt+q$

Given that p = 0. 40 m/s and q = -1. 10 m/s, the equation will become:

$v(t)=2(0.4)t-1.10\\v(t)=0.8t - 1.10$

If the time is t = 1.0 s, the velocity will be:

$v(1) = 0.8 - 1.10\\v(1) = -0.3m/s$

Similarly if t = 4.0ssec, hence:

$v(4) = 3.2 - 1.10\\v(4) = 2.1m/s$

The  average speed between t = 1.0 s and t = 4.0 s will be 2.1+0.3 which is 2.4m/s

Learn more on average speed here: https://brainly.com/question/4931057

Complete question

A mouse runs along a baseboard in your house. The mouse's position as a function of time is given by x(t)=pt 2+qt, with p = 0.40 m/s2and q = -1.10 m/s . Determine the mouse's average speed between t = 1.0 s and t = 4.0 s. I have tried everything and the answer is not 0.40 m/s