Problem: A car travels a distance 100 metre with a constant acceleration and average velocity of 20 metre per second. The final velocity required by the car is 25 metre per second. Find 1) the initial velocity and 2) acceleration of car

Data given:
Distance(s) = 100 metre
Acceleration(a) = ? ( to calculate)
Average velocity(vav)=20 metre per second
final velocity (v)= 25 metre per second
First we will calculate time taken to complete the 100 metre distance with average velocity of 20 metre per second.
t = s/vav
Or t = 100/20
∴ t = 5 s

We know:
a = (v-u)/t
a = (25-u)/5

again we know that:
v2 = u2+2as
Or (25)2=u2+2.a.100
Putting the value of a we have:
Or 625 = u2+200. ((25-u)/5)
Or 625 = u2+1000-40u
Or u2-40u+1000-62 5= 0
Or u2-40u+375 = 0
Or u2-25u-15u+375 = 0
Or u (u-25)-15(u-25)= 0
Or (u-25)(u-15)=0
∴ u=25 u=15 Now when u=25
Or a=0
Which is absurd as the body is moving with constant acceleration. when u=15
a= (25-15)/5
∴ a= 2 m/s2
∴ u = 5 m/s
And a=2 m/s2

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