A car's begin speed is 70 km/h and it accelerates with 6000 km/#h^2# . How many seconds does it take to get from 70 km/h to 120 km/h and what distance did the car need ?

1 Answer
Steve J.
Sep 27, 2017

The speed increase required 72 seconds and 1.9 km.

Explanation:

We can determine the time using the suvat formula
#v = u + a*t#

Plugging in the known data and solving for t

#120 (km)/h = 70 (km)/h + 6000 (km)/h^2*t#

#t = (120 (km)/h - 70 (km)/h)/(6000 (km)/h^2)#

#t = (50 (cancel(km))/cancel(h) ) / (6000 (cancel(km))/(h*cancel(h) #

#t = 0.00833 h#

Converting to seconds: #0.00833 h * (3600 s)/(1 h) = 30 s #

We can determine the distance using the suvat formula
#s = ((u+v)/2)*t#
Notice that this formula calculates the average velocity and multiplies by time. This is legitimate only because the acceleration is constant throughout.

Plugging in the known data
#s = ((70 (km)/h + 120 (km)/h)/2)*0.00833 h #

#s = 95 (km)/h*0.00833 h = 0.79 km#

I hope this helps,
Steve

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