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= (v-u)/(t)\\ \\\implies t = (v-u)/(a) = (40-10)/(8) = (30)/(8) = 3.75 ~sec \\\\s=\left(\frac{u+v}2\right)t=\left(\frac{10+40}2 \right)3.75 = \left((50)/(2)\right)3.75 = 25 * 3.75 = 93.75~m`

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