- #1

RyanH42

- 398

- 16

## Homework Statement

A particle moves so that its equation of motion in vector form given is given by ##\vec{R}=((sint^-1)/2+t/2√(1-t^2))\vec{i}+1/2t^2\vec{j}## , ##0≤t<1##

a)Show that particle moves with a constant speed.

b)Compute ##\vec{v}## and ##\vec{a}##,and verify that ##\vec{v}##.##\vec{a}##=0 (dot product).(As it should be when speed is constant

c)Since the magnitude of speed is constant ,must the magnitude of acceleration also be constant ?

## Homework Equations

##\vec{v}=d\vec{R}/dt##

##\vec{a}=d\vec{v}/dt##

## The Attempt at a Solution

For a), I have to do ##\vec{v}=d\vec{R}/dt## and then I have to do this ##\|\vec{v}\|##.If ##\|\vec{v}\|## this do not contain t it means ##\|\vec{v}\|## is constant

I understad b)

For c)##\vec{v}##.##\vec{a}##=0 this means ##\|\vec{v}\|.\|\vec{a}\|.cosθ=0## we know that ##\|\vec{v}\|## is not zero so there's two option 1) ##\|\vec{a}\|## will be zero or ##cosθ## will be ##0##.If ##cosθ## is zero then there's no need to be constant magnitude of ##\vec{a}##.I think answer is no.Theres a chance to be not constant.

Is my answers are true ?

Thanks