A car is moving along a straight road with un | vedclass

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

Question

(B) Let the acceleration of the car be $a$ and the distance between $P$ and $Q$ be $s$.Using the equation of motion $v^2 = u^2 + 2as$ for the path $PQ

Vedclass · Accepted Answer

$25\sqrt{2}\; km/h$

Vedclass · Answer

(B) Let the acceleration of the car be $a$ and the distance between $P$ and $Q$ be $s$.Using the equation of motion $v^2 = u^2 + 2as$ for the path $PQ$:$40^2 = 30^2 + 2as$$1600 = 900 + 2as$$2as = 700$$as = 350$Let $V$ be the velocity at the midpoint of $PQ$. The distance from $P$ to the midpoint is $s/2$.Using the equation of motion $V^2 = u^2 + 2a(s/2)$:$V^2 = 30^2 + as$$V^2 = 900 + 350$$V^2 = 1250$$V = \sqrt{1250} = \sqrt{625 	imes 2} = 25\sqrt{2}\; km/h$.Alternatively,for uniform acceleration,the velocity at the midpoint $V_{mid}$ is given by:$V_{mid} = \sqrt{\frac{v_P^2 + v_Q^2}{2}}$$V_{mid} = \sqrt{\frac{30^2 + 40^2}{2}} = \sqrt{\frac{900 + 1600}{2}} = \sqrt{\frac{2500}{2}} = \sqrt{1250} = 25\sqrt{2}\; km/h$.

$A$ car is moving along a straight road with uniform acceleration. It passes through two points $P$ and $Q$ separated by a distance $s$ with velocities $30\; km/h$ and $40\; km/h$ respectively. Find the velocity of the car midway between $P$ and $Q$.

Similar Questions

$A$ body starts from rest and moves with constant acceleration for $t$ seconds. It travels a distance $x_{1}$ in the first half of the time and $x_{2}$ in the next half of the time. Then:

Derive the equations of motion for constant acceleration using the method of calculus.

$A$ car moving along a straight line is brought to a stop within a distance of $200 \,m$ and in a time of $10 \,s$. The initial speed of the car is (in $\,ms^{-1}$)

If the decrease in velocity is the same in equal intervals of time,then describe the $x-t$ graph.

The motion of a body is given by the equation $\frac{dv(t)}{dt} = 6.0 - 3v(t)$,where $v(t)$ is speed in $m/s$ and $t$ is in $s$. If the body was at rest at $t = 0$,which of the following statements is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module