A car accelerates from 15km/h to 60km/h in 2 sec . how far does it travel in this time ?

Question

sketch the graph...but please explain how you get this answer!

answer=18.75m

Answer 1

hahaha... that's the wrong answer!

v(avg)=(15+60)/2 = 37.5 km/h

d=2s * 37.5/(60*60) = 20.8 m or about 21 m

Answer 2

Assuming the acceleration is constant, the average speed would be 37.5 kph ((15 + 60) / 2).  If the car was travelling for one hour, it would travel 37.5 kilometers.  Since 2 seconds is approximately .056 percent of 1 hour (2 sec / 3600 sec) (decimal value .00056), multiply 37.5k x .00056 to get .021 kilometers, or 21 meters.

Of course if the acceleration is not constant, the average speed will be more complicated to calculate, but after you have the average speed, the rest in the same.

.

Answer 3

Assuming constant acceleration,

v2 = v1 + at

d2 = d1 + v1t + (1/2)at^2

a = (v2 - v1)/t

d2 = d1 + v1t + (1/2)((v2 - v1)/t)t^2

d2 = d1 + v1t + (1/2)(v2 - v1)t

d2 = d1 + v1(t/2) + v2(t/2)

d2 = d1 + (v1 + v2)(t/2)

d2 = 0 + (15 km/h + 60 km/hr)((2 s)/2)

d2 = (75 km/h)(1,000 m/km)(1 h/3,600 s)(1 s)

d2 = (75 m)3.6 ≈ 20.833 m ≈ 20.8 m

Sorry, but this format does not lend itself to graphics