Physics Question?

Question

A car moving westward along a straight level road increases its velocity uniformly from +19 m/s to +37 m/s in 11.2 seconds.

What is the car's acceleration in m/s^2?
How far did it move while accelerating? Answer in units of m.
What was its average velocity in m/s?

Please explain the steps in solving this problem.

Answer 1

The equations of motion:

v(t)=v0+a*t will solve the first part of this
t=11.2 v0=19 and v(11.2)=37
plug and chug
37=19+a*11.2
a=(37-19)/11.2

the distance is s(t)=s0+v0*t+.5*a*t^2
s0=0
solve for s(11.2)
=19*11.2+.5*(37-19)*11.2
=313.6 m

Note that the average speed is
=(19+.5*(37-19))
=28 m/s

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Answer 2

37=19+11.2a

i don't have a calculator with me, but just subtract 19 from both sides, then divide by 11.2

if you're wondering how i got that, what i did was i used this equation

V[final]=V[initial]+(time)(acceleration)

and plugged in the numbers. don't forget to add the word "west" after the answer -- they asked for velocity

as for it's average velocity, just add 19+37, and divide by two (because it's accelerating uniformly)

and lastly, for the second question (how far), find an equation that includes distance (usually represented by 'X') and plug in the numbers. sorry, i can't remember one off the top of my head.