Question

An automobile is traveling on a long, straight highway at a steady 75.0 mi/h when the driver sees a wreck 190 m ahead. At that instant, she applies the brakes (ignore reaction time). Between her and the wreck are two different surfaces. First there is 100 m of ice, where the deceleration is only 1.30 m/s2 . From then on, it is dry concrete, where the deceleration is a more normal 8.00 m/s2 .

a). What was the car’s speed just after leaving the icy portion of the road?

b).What is the total distance her car travels before it comes to a stop?

c).What is the total time it took the car to stop?

Answer 1

1mi/h=0.447m/s

so,75mi/h=(75*0.447)m/s=33.53m/sec

initial velocity, u=33.53m/s

1^st there is a 100m(x₁) long ice surface on which acceleration, a=-1.30m/s²

let velocity when it leave the icy surface is v,

then,

So,just after leaving the icy portion of road the car has a velocity of 29.4m/s.

and ,let it decelerate on ice for t₁ sec

On the concrete surface ,acceleration

here final velocityand initial velocity

again,

Distance travelled by car before it stops=x₁+x₂=(100+54.02)m=154.02m

now,  

total time it took to stop=t₁+t₂=(3.18+3.675)sec=6.855sec.