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

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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