Question

Displacement ($) of a particle moving in a straight line varies with time tas S = (2t - (?) m, (where tis in second). Find the average velocity (in m/s) of the particle in time interval t = 0 to t = 2 s. =​

Answer 1

a=3t 2 +2t+2

dv=adt

v= 3^3t ^3 + 2^2t^2 +2t

v=t 3+t 2 +2t

at t=0,u=2

att=2

v=t3 +t2 +2t+2

=8+4+2×2+2

=8+4+4+2

=18m/s

Solve any question of Motion in a Straight Line

$\color{blue}{ Answered \ by \ Srijan}$

Answer 2

Complete Question: Displacement (S) of a particle moving in a straight line varies with time as S = 2t² - 3t +5 (where 'S' is n meter and 't' is in seconds). Find the average velocity (in m/s) of the particle in time interval t = 0 to t = 2 seconds.

Given:

Displacement-time function: y = 2t² - 3t + 5

Time interval: t = 0 to t = 2 seconds.

To Find:

Average velocity of the particle in the time interval t = 0 to t = 2 seconds.

Solution:

→ The displacement-time function for a particle is a function that describes the relationship between the displacement of the particle and time. We can say that the displacement-time function describes the instantaneous position of a particle as a function of time.

→ Similarly the displacement-time graph for a particle is the graph between the instantaneous position of the particle and time.

→ In the given question the displacement-time function is: y =  2t² - 3t + 5

• Position at time t = 0 second (y₁) = 2(0)² - 3(0) + 5 = 5 m

• Position at time t = 2 second (y₂) = 2(2)² - 3(2) + 5 = 8 - 6 + 5 = 7 m

→ For a one-dimensional motion we can say that the displacement of the particle is equal to the change in its position. If the particle moves from position S(t₁) to position S(t₂), then its displacement is S(t₂) − S(t₁) over the time interval [t₁, t₂].

∴ The displacement of the particle will be equal to the change in the position of the particle from t = 0 to t = 2 seconds.

∴ Displacement of the particle = 7 - 5 = 2 m

→ The average velocity of a particle is defined as the net displacement of the particle per unit time. We can calculate the average velocity of a particle by dividing the net displacement by the total time.

                        $\therefore Avg. Velocity=\frac{NetDisplacement}{Total Time}$

                        $\therefore Avg. Velocity=\frac{2}{2} =1ms^{-1}$

Hence the average velocity of the particle is equal to 1 ms⁻¹ in the time interval t = 0 to t = 2 seconds.

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