A car is initially moving at 35 km/h along a straight highway. To pass another car, it speeds up to 135 km/h in 10.5 seconds at a constant acceleration.

(a) How large was the acceleration in m/s^2
(b) How large was the acceleration, in units of g= 9.80 m/s^2

Question

A car is initially moving at 35 km/h along a straight highway. To pass another car, it speeds up to 135 km/h in 10.5 seconds at a constant acceleration.

(a) How large was the acceleration in m/s^2
(b) How large was the acceleration, in units of g= 9.80 m/s^2

austin.l · Answer

Well, first we need to translate km/h to m/s. To do that, we need to know dimensional analysis. Are you familiar with it?

girlstudy · Answer

Not really

austin.l · Answer

Okay, so how many meters are in a kilometer?
How many seconds in a minute and how many minutes in an hour?

girlstudy · Answer

1 kilometer = 1000 meters
60secs in a minute
60 mins in an hour

austin.l · Answer

Okay, so

$$\frac{35km}{1hr}\times\frac{1000m}{1km}\times\frac{1hr}{60min}\times\frac{1min}{60sec}=?$$

girlstudy · Answer

35000/3600 ?

girlstudy · Answer

But isnt there a formula we need to follow? like f=MA ? or something

austin.l · Answer

Which would be 9.722m/s

and doing the same for 135km/h would be 37.5m/s

The formula for acceleration is this:

$$a=\frac{\Delta v}{t}$$

Which is change in velocity over time.

Our change in velocity would be 27.778

Our time would be 10.5seconds

so,
$$a=\frac{27.778m/s}{10.5s}$$

which would be 2.6455m/s^2

austin.l · Answer

and for part b, just divide that number by 9.80m/s^2

girlstudy · Answer

ohh i see thank you so much!

austin.l · Answer

No problemo!