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Chapter 2: Q. 48 (page 58)

You are driving to the grocery store at 20 m/s. You are 110 m

from an intersection when the traffic light turns red. Assume

that your reaction time is 0.50 s and that your car brakes with

constant acceleration. What magnitude braking acceleration will bring you to a stop exactly at the intersection?

Short Answer

Expert verified

The magnitude of breaking acceleration to bring the car at a rest is2m/s2.

Step by step solution

01

Given information

Initial velocity u=20m/s, Reaction time t=0.5s, Distance of intersection,d=110m.

02

Calculation

The distance travelled after pressing the brake is, s=uts=20×0.5ms=10m

So the distance traversed before pressing the brake is, D=110-10m=100m.

03

Find the magnitude of acceleration

We can find the acceleration by using the formula,

v2=u2+2Da, where v→finalvelocity,a→acceleration.

The final velocity of the car should be, v=0at the time of stopping.

Therefore, the acceleration to bring the car at a stop can be determined as,

0=u2+2a×100a=-u2200a=-202200a=-2m/s2

Therefore the magnitude of acceleration to bring the car at a rest is 2m/s2.

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Most popular questions from this chapter

The takeoff speed for an Airbus A320 jetliner is 80 m/s. Velocity

data measured during takeoff are as shown.

a. Is the jetliner’s acceleration constant during takeoff?

Explain.

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use trial and error to find the time needed to travel a specific

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sprint 100.0 m. His official time was 0.01 s more than your

answer, showing that this model is very good, but not perfect.

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