Question

Find the instantaneous velocity of the particle described in Figure P2.1 at the following times: (a) t=1.0s, (b) t=3.0s, (c) t=4.5s, and (d) t=4.5s .

Short answer

1. The instantaneous velocity of the particle at is t=1.0s is 5m/s.
2. The instantaneous velocity of the particle at is t=3.0s is -2.5m/s .
3. (a)The instantaneous velocity of the particle at is t= 4.5s is 0 .
4. The instantaneous velocity of the particle at is t=7.5s is 5m/s.

Step-by-step solution

Definition of instantaneous velocity.

The term "instantaneous velocity" refers to the rate of change in location over a relatively brief period of time (almost zero). The SI unit of speed is m/s. Instantaneous speed is the term used to describe the magnitude of the immediate velocity. It has no direction, yet its value is the same as instantaneous velocity.

(a) Determining the instantaneous velocity of the particle at t=1.00s .

$$\begin{gathered} Asshowninfigurep2.1,theins\tan \tan eousvelocityofaparticlemovingin \\ thexaxisisequaltotheslopeofthex-tcurveatthespecifiedtime. \\ Thenwepicktwopointsforeachofthetimeperiodslistedbelow. \\ Thefollowingequationisusedtocalculatetheins\tan \tan eousvelocity \\ v=\frac{∆x}{∆t} \\ Att=1.0s,P(1,5),read(0,0)and(1,5) \\ v=\frac{\left(5-0\right)m}{\left(1-0\right)s} \\ =5m/s. \\ Soatt=1.0sins\tan \tan eousvelocityoftheparticleis5m/s \end{gathered}$$

(b) Determining the instantaneous velocity of the particle at .

$$\begin{gathered} Att=3.0s,P(3,7),read(2,10)and(4,5) \\ v=\frac{\left(5-10\right)m}{\left(4-2\right)s} \\ =-2.5m/s. \\ Soatt=3.0sins\tan \tan eousvelocityoftheparticleis-2.5m/s \end{gathered}$$

(c) Determining the instantaneous velocity of the particle at .

$$\begin{gathered} Att=4.5s,P(4,5),read(4,5)and(5,5) \\ v=\frac{\left(5-5\right)m}{\left(5s-4s\right)} \\ =0 \\ Soatins\tan \tan eousvelocityoftheparticleis0 \end{gathered}$$

(d) Determining the instantaneous velocity of the particle at .

$$\begin{gathered} Att=7.5s,P(7.5,-5),read(7,-5)and(8,0) \\ v=\frac{0-(-5)m}{\left(8s-7s\right)} \\ =+5m/s \\ Soatt=7.5sins\tan \tan eousvelocityoftheparticleis5m/s \end{gathered}$$