Answer to Question #229481 in Physics for Dani

Question

what is the velocity of Hero Honda

bike midway between Rands, when it moving along a straight road with a uniform acceleration.

It passes through two points

R ands, separated by a distance

with

velocity 30 km/h and 40 km/h

Answer 1

Let the distance between two points be $d$, then the distance from the initial location to the midpoint is $d/2$. Let also $v_i = 30km/h$ and $v_f = 40km/h$ be the initial and final speeds respectively.

According to the kinematic equation (see https://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations), the acceleration of such motion is given as follows:

$$v_f^2 = v_i^2 + 2ad\\ a = \dfrac{v_f^2 - v_i^2}{2d}$$

Using the same equation but this time for the midpoint, obtain the velocity at this point:

$$v_{mid}^2 = v_i^2 + 2a\dfrac{d}{2} = v_i^2 + ad$$

Substituting the expression for $a$, get:

$$v_{mid} = \sqrt{v_i^2 + \dfrac{v_f^2 - v_i^2}{2d}\cdot d } = \sqrt{\dfrac{v_i^2+v_f^2}{2}}\\ v_{mid} = \sqrt{\dfrac{30^2+40^2}{2}} \approx 35km/h$$

Answer. 35 km/h.