Question

You are driving along the street at the speed limit ($35mph$) and $50$ meters before reaching a traffic light you notice it becoming yellow. You accelerate to make the traffic light within the $3$ seconds it takes for it to turn red. What is your speed as you cross the intersection? Assume that the acceleration is constant and that there is no air resistance.

• A. $30mph$
  
• B. $40mph$
  
• C. $50mph$
  
• D. $60mph$
  

Answer 1

The correct option is B $40mph$

This is the motion with constant acceleration. If the acceleration of the car is $a$ then we can write the expression for traveled distance.

$s=ut+\frac{1}{2}a{t}^2$

Here,

$u=$initial velocity $=35mph$

$=15.645㎧$

After $3$ sec, the car travels distance $50$ meters. Then we can find acceleration

$a=\frac{2(s-v_{0}t)}{t^2}$

$=\frac{2(50-15.645\times 3)}{3^2}$

$=\frac{2(50-46.935)}{9}$

$=0.6811㎨$

From relation, $v=u+at$

$=15.6+0.68\times 3$

$=17.64㎧$

i.e., $=40mph$