Answer to Question #229481 in Physics for Dani

Question #229481
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
1
Expert's answer
2021-08-25T17:24:17-0400

Let the distance between two points be dd, then the distance from the initial location to the midpoint is d/2d/2. Let also vi=30km/hv_i = 30km/h and vf=40km/hv_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:


vf2=vi2+2ada=vf2vi22dv_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:


vmid2=vi2+2ad2=vi2+adv_{mid}^2 = v_i^2 + 2a\dfrac{d}{2} = v_i^2 + ad

Substituting the expression for aa, get:


vmid=vi2+vf2vi22dd=vi2+vf22vmid=302+402235km/hv_{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.


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