An object attached to a horizontal spring is oscillating back and forth along a frictionless surface. The maximum speed of the object is 1.54 m/s, and its maximum acceleration is 8.13 m/s2. How much time elapses betwen an instant when the object's speed is at a maximum and the next instant when its acceleration is at a maximum

Explanation:

The spring will move under SHM .

Maximum speed is at the middle equilibrium position . Maximum acceleration is when the particle is at one of the extreme position . So time gap between the two position is one fourth of time period of oscillation .

=  T / 4

If A be the amplitude and ω be angular velocity

ω A =  maximum velocity = 1.54

ω² A = maximum acceleration = 8.13

dividing

ω = 5.28

2π / T = 5.28

T = 1.189

T / 4 = 0.3 s.

if the thermos has a vacuum innner, then heat through conv currents and conduction are reduced = vacuum flask

v 154.9= 0.9 length length s little over 154.9cm