Do you understand physics acceleration?

Question

A car accelerates uniformly from rest to a speed of 40.0 mi/h in 12.0s. Find a) the distance the car travels during this time and b) the constant acceleration of the car. I'm trying to study for a test and I cannot figure out this answer. Other students from my class cannot figure it out as well. Any help would be great! Thank you so much!

Answer 1

acceleration is changing velocity over time

when velocity changes, there is an acceleration.
the velocity change from 0mi/hr to 40mi/hr, again, there is an acceleration which we are going to find

notice that the time is in second but the velocity is in hr (mi/hr).
we have to convert 40mile/hr to m/s

40mile/hr --> 17.92m/s

Vf = at + Vi
17.92m/s = a(12s) + 0m/s
a= 1.49m/s^2

x=1/2at^2
x= 1/2(1.49m/s^2)(12s)^2
x = 107.28m

Answer 2

Your final edited problem: This is a good vector problem, if you pay careful attention to direction and signs. Let the direction upward be +ve. Then: v - final velocity - what you are solving for u = initial velocity in this case +30m/s a = acceleration In this case -9.81m/s² (-ve because acceleration is downward.) t = time which has no direction, but taken as +ve 9 seconds. Substitute into equation: v =u+at v = 30 +(-9.81)9 V = 30-88.29 v = -58.29m/s The negative sign tells you that the velocity is downwards: Answer: the stone has a velocity of 58.3m/s downwards

Answer 3

It is easier to answer part b) first. The acceleration is 40mi/h/12sec = 40mi/3600sec/12sec = 40mi/43200sec^2

= 9.26x10^-4mi/sec^2

now, the distance travelled in 12 seconds is given by:

s=ut+1/2 at^2

u=0 (since the car is stationary to begin with)

so, s=1/2 x 9.26x10^-4 x 12^2

= 0.5 x 9.26x10^-4 x 144 mi

= 0.066666666667 mi or 1/15 of a mile

Answer 4

it like this, use the linear motion equation.
v^2 = u^2 +2a(s-s0) ...1
v=u+at ...2
40mi/hr = 1/90 mi/s
a) first find the accleration of the car using equation 2, a = (v-u)/t.
a=((1/90)-0)/12=1/1080mi/s^2

then, use the equation 1 to find the distance, s.
(1/90)^2 = 0^2 + 2(1/1080)(s-0)
s=1/15 miles

b) the constant acceleration of the car is same as calculated using equation 2 above. a=1/1080 mi/s^2


v=final velocity, u=initial velocity, a=acceleration, s=distance travel, s0=initial distance (which in this example, it didn't have initial distance. so s0=0 in this example.), and t=time.


*it simple is it. just substitute in your value into the equations and the answer is out. regards. best of luck for your test. =)

Answer 5

40 mph = 40 × 5280 ft/3600 s = 58.67 ft/s (fps). I assume from problem statement you need to use engineering (english) units.

a) Distance is the product of average velocity and time. Since this is accelerated motion, velocity isn't constant; increases (linearly) with time. Initially, it is 0 fps; after 12 s, it is 58.67 fps. Average velocity is thus,

ṽ = (0 + 58.67)/2 = 29.33 fps,

so distance traveled in 12 s at 29.33 fps, average, is

d = 29.33 ft/s × 12 s = 352 ft.

b) Acceleration is the time rate of change of velocity. Velocity changes from 0 to 58.67 fps; in 12 s. Thus,

a = 58.67 ft/s / 12 s = 4.89 ft/s².

You may use d = ½ at² as a check:

d = ½ × 4.89 ft/s² × 12² s² = 352 ft.

Answer 6

pzkfw5g is wrong. Vave = (Vo+Vf)/2 = 20 mph

So Steve N's idea on how to get the answer to a) is good. You will have to convert between hours and seconds.

Then for b) use s = (1/2)*a*t^2 Solve for a, you now know all the other pieces.

I agree with the answers of cloudy and Mez.

Answer 7

Distance traveled is average velocity x time.

If the velocity changes uniformly,
Average velocity = ½ of (Initial speed + final speed).

In the problem average speed is 20 miles / hour

Distance = (20 miles / hour ) x 12 second.

One hour = 3600 second.

Therefore distance = (20 /3600) x 12 miles

= 0.067 mile.
= 0.067 x 5280 = 352 foot.
------------------------------------------------------------
Acceleration is {change in velocity / time}.

Change in velocity = (40 -0) miles per hour

= (40/3600) miles per second.
= 0.0111 miles per second
a = (0.0111 /12) miles per (second) ^2.

a = 4.9 foot / s^2.

Answer 8

THE AVERAGE SPEED WAS 20 MPH. HOW FAR WOULD YOU TRAVEL IN 12 SECONDS AT 20 MPH.

MAKE SURE TO GET YOUR UNITS RIGHT. CONVERT MPH TO FEET PER SECOND.