A point moves with uniform acceleration and v | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $u_1, u_2, u_3$ and $u_4$ be the velocities at times $t = 0, t_1, (t_1 + t_2)$ and $(t_1 + t_2 + t_3)$ respectively,and let $a$ be the uniform

Vedclass · Accepted Answer

$(v_1 - v_2) : (v_2 - v_3) = (t_1 + t_2) : (t_2 + t_3)$

Vedclass · Answer

(B) Let $u_1, u_2, u_3$ and $u_4$ be the velocities at times $t = 0, t_1, (t_1 + t_2)$ and $(t_1 + t_2 + t_3)$ respectively,and let $a$ be the uniform acceleration.The average velocities are given by:$v_1 = \frac{u_1 + u_2}{2}, v_2 = \frac{u_2 + u_3}{2}, v_3 = \frac{u_3 + u_4}{2}$Using the equation of motion $v = u + at$,we have:$u_2 = u_1 + at_1$$u_3 = u_1 + a(t_1 + t_2)$$u_4 = u_1 + a(t_1 + t_2 + t_3)$Now,calculate the differences:$v_1 - v_2 = \frac{u_1 + u_2 - u_2 - u_3}{2} = \frac{u_1 - u_3}{2} = \frac{u_1 - (u_1 + a(t_1 + t_2))}{2} = -\frac{a(t_1 + t_2)}{2}$$v_2 - v_3 = \frac{u_2 + u_3 - u_3 - u_4}{2} = \frac{u_2 - u_4}{2} = \frac{(u_1 + at_1) - (u_1 + a(t_1 + t_2 + t_3))}{2} = -\frac{a(t_2 + t_3)}{2}$Taking the ratio:$\frac{v_1 - v_2}{v_2 - v_3} = \frac{-a(t_1 + t_2) / 2}{-a(t_2 + t_3) / 2} = \frac{t_1 + t_2}{t_2 + t_3}$Thus,$(v_1 - v_2) : (v_2 - v_3) = (t_1 + t_2) : (t_2 + t_3)$.

$A$ point moves with uniform acceleration and $v_1, v_2$ and $v_3$ denote the average velocities in the three successive intervals of time $t_1, t_2$ and $t_3$. Which of the following relations is correct?

Similar Questions

The displacement of a particle after time $t$ is given by $x = (k/b^2)(1 - e^{-bt})$ where $b$ is a constant. What is the acceleration of the particle?

In a car race on a straight road,car $A$ takes a time $t$ less than car $B$ at the finish and passes the finishing point with a speed $v$ more than that of car $B$. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$ respectively. Then $v$ is equal to

$A$ particle moves along the $x$-axis as $x = 4(t-2) + a(t-2)^2$. Which of the following statements is true?

$A$ particle is projected with velocity $v_0$ along the $x-$axis,and its deceleration is given by $a = -\alpha x^2$. The distance at which the particle stops is

$A$ body moves on a frictionless plane starting from rest. If $S_{n}$ is the distance moved between $t=n-1$ and $t=n$,and $S_{n-1}$ is the distance moved between $t=n-2$ and $t=n-1$,then the ratio $\frac{S_{n-1}}{S_n}$ is $\left(1-\frac{2}{x}\right)$ for $n=10$. The value of $x$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module