Question

Problem 2. 2 .The particle P moves along the curved slot, a portion of which is shown. Its distance in meters measured along the slot is given by s = t^2/ where t is in seconds. The particle is at A when t = 2.00s and at B when t = 2.20s. Determine the magnitude a_avg of the average acceleration of P between A and B. Also express the acceleration as a vector a_avg using unit vectors i and j.​

Answer 1

Magnitude of average acceleration  $a_{avg}$=2.75 units

Average acceleration $a_{avg}=$ $2.265 i- 1.58j$

We're given that $s=\frac{t^2}{4}$

And partice is at A at t=2 s and at B at t= 2.2s

Instantaneous velocity $\frac{ds}{dt} =\frac{t}{2}$

Velocity at A  ($V_{a}$) at 2s = $\frac{t}{2}$ or  $\frac{t}{2}Cos \frac{\pi}{3} i+ \frac{t}{2}Sin \frac{\pi}{3}j=\frac{i+\sqrt{3} j}{2}$

Velocity at B  ($V_{b}$) at 2.2s =$\frac{t}{2}$ or $\frac{t}{2}Cos \frac{\pi}{6} i+ \frac{t}{2}Sin \frac{\pi}{6}j=\frac{\sqrt{3}i+j }{2}$

Average acceleration = $\frac{V_{b}-V{a}}{t}$ =$2.265 i- 1.58j$

magnitude = $\sqrt{(2.265)^2- (1.58)^2}$ = $2.75$

Learn more about Acceleration here:

https://brainly.com/question/460763

#SPJ10