Motion in One DimensionProblems MC Questions

2

A motorcycle is moving with a speed v when the rider applies the brakes, giving the motorcycle a constant deceleration. During a time t, immediately after braking begins, the speed decreases to v/2. What distance does the motorcycle travel from the instant braking begins until the motorcycle stops?

Stopping a motorcycle 1

2

2

t

v )E(

tv

)D( vt )C( vt )B( t

v )A(

Let v = 22.0 m/s and t = 4.00 s, calculate the distance required to stop the motorcycle.

m 88 )E( m 48 )D(

m 87 )C( m 47 )B( m 86 )A(

A sprinter acquires a top speed v while running a race length D. If the sprinter starts from rest and accelerates at a constant rate, he is able to reach his top speed in a distance d. He is then able to maintain this top speed for the remainder of the race. What is his time required for the sprinter to run the race?

Running a Race 2

vd

)E( v

dD )D(

2vdD

)C( vD

)B( v

dD )A(

If v = 11.0 m/s, d = 12 m, and D = 100 m, calculate the time required for the sprinter to run the race.

s 0.41 )E( s 0.21 )D(

s 0.01 )C( s .89 )B( s .69 )A(

On a dry road a car with good tires is able to brake with a

constant deceleration of 4.92 m/s2. If the car is initially traveling at 24.6 m/s,(a) how much time is required to stop?

3

s 52 )E( s 02 )D(

s 51 )C( s 01 )B( s .05 )A(

(b) how far does it travel in this time?

m 07 )E( m 66 )D(

m 26 )C( m 85 )B( m 45 )A(

The maximum acceleration of a subway train is , and subway stations are located a distance d apart, (a) what is the maximum speed a subway train can attain between stations?

a

4

da )E( da

)D(

ad

)C( da )B( ad

)A(

(b) what is the travel time between stations?

ad

2 )E( ad2 )D(

ad

)C( da

2 )B( da

)A(

Solutions

A motorcycle is moving with a speed v when the rider applies the brakes, giving the motorcycle a constant deceleration. During a time t, immediately after braking begins, the speed decreases to v/2. What distance does the motorcycle travel from the instant braking begins until the motorcycle stops?

ax2vv 2o

2

x t2

v2v0 2

t2v

a

t

v2v

a

vtx

Stopping a motorcycle

vv0v

o

tv

a

1

A motorcycle is moving with a speed of 22.0 m/s when the rider applies the brakes, giving the motorcycle a constant deceleration. During a time of 4.00 s, immediately after braking begins, the speed decreases to 11.0 m/s. What distance does the motorcycle travel from the instant braking begins until the motorcycle stops?

vtx

Stopping a motorcycle

s 4.00 m/s 22.0x

m .088x

1

t 2

vvx fi

v

tt1 t2

dD d

vd2

t1

tx

v

21 ttt

The time required to run the race t = t1 + t2

Running a Race

1t 2v0

d

2tdD

v

vdD

t2

vdD

vd2

t

vdD

t

During acceleration Constant speed

2

The time required for the sprinter to run the race?

Running a Race

vdD

t

11

tt1 t2

12 m88 m

m/s 11m 12m 100

t s 2.10

2

On a dry road a car with good tires is able to brake

with a constant deceleration of 4.92 m/s2. If the car is initially traveling at 24.6 m/s,(a) The time required to stop the car.

atvv o

a

vt o 2m/s 4.92

m/s 24.6

s 0.5t

atv0 o

3

On a dry road a car with good tires is able to brake

with a constant deceleration of 4.92 m/s2. If the car is initially traveling at 24.6 m/s,(b) The distance the car travels in this time.

ax2vv 2o

2

a2

vx

2o

2

2

m/s .9242

m/s 24.6

m 5.61x

3

ax2v0 2o

2

ax2vv 2o

2

advmax

vmax

t

a

(s)

2d

2d

2d

a20v 22max

a) The maximum speed a subway train can attain between stations4

2at

tvx2

o

ad

th

vmax

t

a

(s)

2d

2d

2

att0

2d 2

hh

a) The travel time between stations.

Time to travel half way

ad

2t2t htotal

4

Total time for trip