Question

A car initially travels at 10 m/s when passing the "acceleration line". The car then accelerates Q. at 8m/s2 until reaching a final velocity of 40 m/s. What is the car's displacement during the acceleration?
answer choices
3.75 m
93.75 m
100 m
1590 m​

Answer 1

$\text{Given that,}\\\\\text{Initial velocity,}~ u = 10 ~ms^{-1}\\\\\text{Final velocity,}~ v = 40 ~ ms^{-1}\\\\\text{Acceleration,}~ a = 8 ~ ms^{-2}\\ \\\text{Time ,}~ t =?\\\\\text{Displacement, }~ s = ?\\\\\text{We know that,}\\\\a= \dfrac{v-u}{t}\\ \\\implies t = \dfrac{v-u}{a} = \dfrac{40-10}{8} = \dfrac{30}{8} = 3.75 ~sec \\\\s=\left(\dfrac{u+v}2\right)t=\left(\dfrac{10+40}2 \right)3.75 = \left(\dfrac{50}{2}\right)3.75 = 25 \times 3.75 = 93.75~m$

$\text{Hence, the displacement of the car is 93.75 m}$