Example 1: A particle accelerates uniformly from rest at 6m/s² for 8s and then decelerates uniformly to rest in the next 5s. Determine the magnitude of the deceleration (WAEC)

$$ a = 6m/s² $$ $$ \text{time for acceleration}= 8s $$ $$ \text{initial velocity, }u = 0 $$ $$\text{final velocity, }v = ? $$ $$\text{time for deceleration} = 5s $$ $$\text{To find deceleration, find v} $$ $$ v = u + at $$ $$ v = 0 + 6 × 8 $$ $$ v = 48m/s $$ $$\text{the deceleration,a in the next 5s is: }$$ $$ \text{since the body comes to rest in 5s} $$ $$ u = 48m/s² $$ $$ v = 0 $$ $$ a = \frac{v - u}{t} $$ $$ a = \frac{0 - 48} {5} $$ $$ a = \frac{-48} {5} $$ $$ a = -9.6m/s² $$

Example 2: A body starts from rest and accelerates uniformly at 5m/s² until it attains a velocity of 25m/s. Calculate the time taken to attain this velocity (WAEC)

$$ a = 5m/s² $$ $$ u = 0 $$ $$ v = 25m/s $$ $$ t = ? $$ $$ a = \frac{v - u}{t} $$ $$ t = \frac{v - u}{a} $$ $$ t = \frac{25 - 0} {5} $$ $$\text{time taken} = 5s $$

Example 3: If a car starts from rest and moves with uniform acceleration of 10m/s² for 10 seconds. Calculate the distance it covers in the last one second (JAMB)

$$ a = 10m/s² $$ $$ {t_1} = 10s $$ $${t_2} = 10 - 1 = 9s $$ $$ u = 0 $$ $$ s = ut + \frac{1}{2}at² $$ $$ s = 0 × 9 + \frac{1}{2} × 10 × ({t_1}²- {t_2}²)$$ $$ s = \frac{1}{2} × 10 × ((10)² - (9)²)$$ $$ s = \frac{1}{2} × 10 × (100 - 81) $$ $$ s = \frac{1}{2} × 10 × 19 $$ $$ s = \frac{190}{2} $$ $$ s = 95m $$

Example 4 : A body accelerates uniformly from rest at 2m/s². Calculate its velocity after travelling 9m.