Answer to Question #176537 in Physics for Chimka

Question #176537

The speed if a car increased from 36km/h to 96km/h in 0.6km.how long did this take and what was the acceleration


1
Expert's answer
2021-03-29T08:57:29-0400

The acceleration of the car by definition is:


a=vfvita = \dfrac{v_f-v_i}{t}

where vf=96km/h=803m/sv_f = 96km/h = \dfrac{80}{3}m/s is the final speed of the car, vi=36km/h=10m/sv_i = 36km/h = 10m/s is the initial speed of the car, and tt is the time of acceleration.

The distance d=0.6km=600md = 0.6km = 600m travelled under the constant acceleration is given by the kinematic equation:


d=vit+at22d = v_it+\dfrac{at^2}{2}

Substituting aa, obtain:


d=vit+vft2vit2=(vf+vi)t2t=2dvf+vit=260080/3+1032.7sd = v_it + \dfrac{v_ft}{2} - \dfrac{v_it}{2}= \dfrac{(v_f+v_i)t}{2}\\ t = \dfrac{2d}{v_f+v_i} \\ t = \dfrac{2\cdot 600}{80/3+10}\approx 32.7s

Answer. 32.7 s


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