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(v_{av})=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/v_{av}

Or t = 100/20

∴ t = 5 s

We know:

a = (v-u)/t

a = (25-u)/5

again we know that:

v^{2} = u^{2}+2as

Or (25)^{2}=u^{2}+2.a.100

Putting the value of a we have:

Or 625 = u^{2}+200. ((25-u)/5)

Or 625 = u^{2}+1000-40u

Or u^{2}-40u+1000-62 5= 0

Or u^{2}-40u+375 = 0

Or u^{2}-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

a=(25-25)/5

Or a=0

Which is absurd as the body is moving with constant acceleration.
when u=15

a= (25-15)/5

∴ a= 2 m/s^{2}

∴ u = 5 m/s

And a=2 m/s^{2}

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