A point moves with uniform acceleration and u | vedclass

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

Question

Let $u_{1}, u_{2}, u_{3}$ and $u_{4}$ be the velocities at times $t=0, t_{1},\left(t_{1}+t_{2}\right)$ and $\left(t_{1}+t_{2}+t_{3}\right)$ respective

Vedclass · Accepted Answer

$(\upsilon_ 1 -\upsilon_ 2) : (\upsilon_ 2 -\upsilon_ 3) = (t_1 + t_2) : (t_2 + t_3)$

Vedclass · Answer

Let $u_{1}, u_{2}, u_{3}$ and $u_{4}$ be the velocities at times $t=0, t_{1},\left(t_{1}+t_{2}\right)$ and $\left(t_{1}+t_{2}+t_{3}\right)$ respectively. Let 'a' be the acceleration.

Now, $\quad \mathrm{v}_{1}=\frac{\mathrm{u}_{1}+\mathrm{u}_{2}}{2}, \quad \mathrm{v}_{2}=\frac{\mathrm{u}_{2}+\mathrm{u}_{2}}{2}$ and $\mathrm{v}_{3}=\frac{\mathrm{u}_{2}+\mathrm{u}_{4}}{2}$

Also $\quad \mathrm{u}_{2}=\mathrm{u}_{1}+\mathrm{at}_{1}, \mathrm{u}_{3}=\mathrm{u}_{1}+\mathrm{a}\left(\mathrm{t}_{1}+\mathrm{t}_{2}\right)$ and $\quad \mathrm{u}_{4}=\mathrm{u}_{1}+\mathrm{a}\left(\mathrm{t}_{1}+\mathrm{t}_{2}+\mathrm{t}_{3}\right)$

By solving, we get $\frac{v_{1}-v_{2}}{v_{2}-v_{3}}=\frac{\left(t_{1}+t_{2}\right)}{\left(t_{2}+t_{3}\right)}$

A point moves with uniform acceleration and $\upsilon _1,\upsilon _2$ and $\upsilon _3$ 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

Let $v$ and a denote the velocity and acceleration respectively of a particle in the dimensional motion

A parachutist drops freely from an aeroplane for $10\,s$ before the parachute opens out. Then he descends with a net retardation of $2.5\, m/s^2$. If he bails out of the plane at a height of $2495\, m$ and $g = 10\, m/s^2$, hit velocity on reaching the ground will be .......$m/s$

A bus is moving with a velocity $10 \,m/s$ on a straight road. A scooterist wishes to overtake the bus in $100\, s$. If the bus is at a distance of $1 \,km$ from the scooterist, with what velocity should the scooterist chase the bus......... $m/s$

The displacement $x$ of a particle varies with time $t$ as $x = a{e^{ - \alpha t}} + b{e^{\beta t}}$ , where $a, b, \alpha$ and $\beta $ are positive constants. The velocity of the particle will

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