An automobile traveling along a straight road increases its speed from 30.0 m/s to 50.0 m/s in a distance of 180 m. If the acceleration is constant, how much time elapses while the auto moves this distance

4.5sec

Explanation:

From the question above, the following are the parameters that are given

u = 30m/s

v = 50m/s

s = 180m

First of all we have to find the acceleration by using the third equation of motion

V^2 = U^2 + 2as

50^2 = 30^2 + 2 (a) (180)

2500 = 900 + 360a

Collect the like terms

2500-900 = 360a

1600=360a

Divide both sides by the coefficient of a which is 360

1600/360=360a/360

a = 4.44m/s

The next step is to find the time. To do this we will have to use the first equation of motion

v = u + at

50 = 30 + 4.44t

Collect the like terms

50-30 = 4.44t

20 = 4.44t

Divide both sides by the coefficient of t which is 4.44

20/4.44 = 4.44t/4.44

t = 4.5sec

Hence 4.5secs elapses while the auto moves at a distance of 180m