Question

Let’s allow ourselves to be a little more optimistic with our bus passengers. Earlier in the movie Sandy has to make the bus jump a large gap in the roadway. She is moving at 60 mph and as an astute physicist, she knows she must get the bus moving at a minimum of 80 mph within a half mile if she is to make the jump. Assuming constant acceleration, when does the bus make the jump after it begins to accelerate? (1 mile = 1609.34 m)

Answer 1

Answer:

25.71486 seconds

Explanation:

t = Time taken

u = Initial velocity = 60 mph

v = Final velocity = 80 mph

s = Displacement = 0.5 mile

a = Acceleration

Converting to m/s

$60\times \dfrac{1609.34}{3600}=26.8223\ m/s$

$80\times \dfrac{1609.34}{3600}=35.7631\ m/s$

From equation of motion

$v^2-u^2=2as\\\Rightarrow a=\dfrac{v^2-u^2}{2s}\\\Rightarrow a=\dfrac{35.7631^2-26.8223^2}{2\times \dfrac{1609.34}{2}}\\\Rightarrow a=0.34769\ m/s^2$

$v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{35.7631-26.8223}{0.34769}\\\Rightarrow t=25.71486\ s$

Time taken is 25.71486 seconds