A Honda Civic travels in a straight line along a road. The car’s distance x...

kloseyq

kloseyq

Answered

2022-01-12

A Honda Civic travels in a straight line along a road. The car’s distance x from a stop sign is given as a function of time t by the equation x(t)=αt2βt3, where α=1.50 ms2 and β=0.0500 ms3
Calculate the average velocity of the car for each time interval:
a) t=0 to t=2.00s
b) t=0 to t=4.00 s
c) t=2.00s to t=4.00s

Answer & Explanation

chumants6g

chumants6g

Expert

2022-01-13Added 33 answers

Step 1
First we have to calculate the distance x at each t.
x(0)=Zero m
x(2)=1.50(2)20.0500(2)3=5.6m
x(4)=1.50(4)20.0500(4)3=20.8m
The average velocity is the displacement divided by the time interval at which this displacement happened.
vx, avg=ΔxΔt
Δx=xfxi
Δt=tfti
Step 2
a) vx, avg=xfxitfti
x(0)=Zero m
x(2)=1.50(2)20.0500(2)3=5.6m
vx, avg=5.6020
=2.8ms
Step 3
b) x(0)=Zero m
x(4)=1.50(4)20.0500(4)3=20.8m
vx, avg=20.8040
=5.2ms
Step 4
c) x(2)=1.50(2)20.0500(2)3=5.6m
x(4)=1.50(4)20.0500(4)3=20.8m
vx, avg=20.85.642
=7.6ms
Mary Herrera

Mary Herrera

Expert

2022-01-14Added 37 answers

Step 1
a) The equation for cars
nick1337

nick1337

Expert

2022-01-14Added 573 answers

Step 1
a) The position of the car as a function of time t is given by
x(t)=αt2βt3
where
α=1.50m/s2β=0.05m/s3
The average velocity is given by the ratio between the displacement and the time taken:
v=ΔxΔt
The position at t = 0 is:
x(0)=α×02β×03=0
The position at t = 2.00 s is:
x(2)=α×22β×23=5.6m
So the displacement is
Δx=x(2)x(0)=5.60=5.6m
The time interval is
Δt=2.0s0s=2.0s
And so, the average velocity in this interval is
v=5.6m2.0s=2.8m/s
b) The position at t = 0 is:
x(0)=α×02β×03=0
While the position at t = 4.00 s is:
x(4)=α×42β×43=20.8m
So the displacement is
Δx=x(4)x(0)=20.80=20.8m
The time interval is
Δt=4.000=4.0s
So the average velocity here is
v=20.84.0=5.2m/s
c) The position at t = 2 s is:
x(2)=α×22β×23=5.6m
While the position at t = 4 s is:

x(4)=α×42β×43=20.8m
So the displacement is
Δx=20.85.6=15.2m
While the time interval is
Δt=4.02.0=2.0s
So the average velocity is
v=15.22.0=7.6m/s

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