Question

A car travels a distance 100m with a constant acceleration and average velocity of 20 m/s. the final velocity acquired by the car is 25 m/ s. find(1) the initial velocity (2) acceleration of the car

Answer 1

s=100m

v=25m\s

average velocity=20m/s

Average velocity=u+v/2

20=u+25 /2

40=u+25

u=40-25=15m/s

Answer 2

Given

Total distance (S) = 100m

Average velocity = 20m/s

Final velocity (v) = 25m/s

i) Initial velocity

$\rm{we \:know} \\ \rm{ \: average \: velocity \: = \frac{v + u}{2} }$

$\implies\rm{20 = \frac{25 + u}{2} }$

$\implies\rm{20 \times 2 = {25 + u}}$

$\implies\rm{ u= 40 - {25 }}$

$\rm\fbox{ \therefore \: initial \: velocity = 15m {s}^{ - 1} }$

ii) Acceleration

$\rm \: From \: Equation \: of \: motion \: {v}^{2} - {u}^{2} = 2aS$

$\implies \rm \: {25}^{2} - {15}^{2} = 2a \times 100$

$\implies \rm \: 625 - 225 = 200 a$

$\implies \rm \: 400 = 200 a$

$\implies \rm \: a = \frac{400}{200}$

$\rm\fbox{ \therefore \: acceleration = 2m {s}^{ - 2} }$