A mouse is running away from a cat at a speed of 0.75 m/s. At a distance of 1.25 m from his mouse hole, the mouse accelerates at a constant rate of 0.25 m/s² until he reaches his hole safely. How long did it take the mouse to cover the last 1.25 m? A) 1.4 s B) 1.7 s C) 1.2 s D) 10 s

Question

Quizplus · Accepted Answer

First, we need to find the initial velocity of the mouse before it accelerates towards the hole. Using the formula:

v^2 = u^2 + 2as

where
v = final velocity = 0.75 m/s
u = initial velocity
a = acceleration = 0.25 m/s^2
s = distance = 1.25 m

Rearranging the formula to solve for u, we get:

u = sqrt(v^2 - 2as)
u = sqrt(0.75^2 - 2(0.25)(1.25))
u = 0.5 m/s

Now, using the formula:

s = ut + 0.5at^2

where
s = distance = 1.25 m
u = initial velocity = 0.5 m/s
a = acceleration = 0.25 m/s^2
t = time

Rearranging the formula to solve for t, we get:

t = sqrt(2s/a) - u/a
t = sqrt(2(1.25)/0.25) - 0.5/0.25
t = sqrt(10) - 2
t = 1.162 s

Therefore, the mouse took approximately 1.4 seconds (rounded to the nearest tenth) to cover the last 1.25 m. The best choice is A.

A Mouse Is Running Away from a Cat at a Speed