Answer to Question #152221 in Physics for kasu

Question #152221
A car starts at a speed of 30 meters per second and travels at a uniform acceleration of 10 seconds and achieves a speed of 60 meters per second. How far did the car travel?
1
Expert's answer
2020-12-21T11:00:58-0500

The distance travelled under the uniform acceleration aa is:


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

where vi=30m/sv_i = 30m/s is the initial speed, and t=10st = 10s is the time.

By definition, acceleration is:


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

where vf=60m/sv_f = 60m/s. Substituting aa into the first equation, obtain:


d=vit+12t(vfvi)=12t(vf+vi)d=1210(60+30)=450md = v_it + \dfrac12t(v_f - v_i) = \dfrac12t(v_f+v_i)\\ d = \dfrac12\cdot 10\cdot (60+30) = 450m

Answer. 450 m.


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