A car travels a distance 100 m with a constant acceleration and average velocity of 20 m s^-1. The final velocity acquired by the car is 25 m s^-1.

Find:

(i) the initial velocity and

(ii) acceleration of car.

(i) Given,

v = 25 m s^-1

As we know,

average velocity = $\dfrac{u+v}{2}$ = 20 m s^-1

Substituting the value we get,

$\dfrac {u + v}{2} = 20 \\[0.5em] \dfrac{u + 25}{2} = 20 \\[0.5em] u + 25 = 20 \times 2 \\[0.5em] u + 25 = 40 \\[0.5em] \Rightarrow u = 40 - 25 = 15 m s^{-1} \\[0.5em]$

Hence, initial velocity of the car is 15 m s^-1

(ii) We know, from the equation,

v² = u² + 2aS

S = 100 m

v = 25 m s^-1

u = 15 m s^-1

Substituting the values in the formula above we get,

${25} ^2 = {15}^2 + (2 \times a \times 100) \\[0.5em] 625 = 225 + (200 \times a) \\[0.5em] 625 - 225 = (200 \times a) \\[0.5em] 400 = (200 \times a) \\[0.5em] \Rightarrow a = \dfrac {400}{200} \\[0.5em] \Rightarrow a = 2 \text{m s}^{-2}\\[0.5em]$

Hence, acceleration of car = 2 m s^-2