Acceleration: Assuming constant acceleration, compute....

[doggypoo123]

The manufacturer of an automobile advirtises that it takes 14 seconds to accelerate from 26 kilpmeters per hour to 77 kilometers per hour. Assuming constant acceleration compute the following:

a) The acceleration in meters per second per second.
b) The distance traveled during 14 secounds.

I know the answers are (a) 1.01 m/sec^2 and (b) 200.28 meters. But I don't know they got them. Can anyone show me?

 

[TchrWill]

the manufacturer of an automobile advirtises that it takes 14 seconds to accelerate from 26 kilpmeters per hour to 77 kilometers per hour. Assuming constant acceleration compute the following:
a) The acceleration in meters per second per second.
b) The distance traveled during 14 secounds.

i know the answer is (a) 1.01 m/sec^2
(b) 200.28 meters
i just dont know they got it. can anyone show me?

Vo = 26k/h(1000m/km)/3600sec = 7.22 m/s
Vf = 77(1000)/3600 = 21.388 m/s
From Vf = Vo + at, 21.388 = 7.22 + a(14) making a = 1.01 m/s/s.

The distance traveled derives from s = Vot += at^2/2 or
s = 7.22(14) + (1.01)(14^2)/2 = 200.06 met.

 

[morson]

Assuming straight-line motion, also:

v = u + at, where a and v are the acceleration and velocity at any time, respectively, and u is the initial velocity.

If we measure time from the moment the automobile began to accelerate, then u = 26 km/h. Hence, v = at + 26, where t is in hours, v is in km/hr.

At t = 7/1800 (14 seconds is 7/1800 of an hour), v = 77:

51 = (7/1800)a ==> a = 51 * 1800/7 = (91800/7)km/hr/hr. Now convert.

 

[doggypoo123]

thanks alot

 

[sky2rain]

I guess one thing you guys left out is why you assumed all these. Becuase when advertising an automobile the manufacture is always trying to give you a mental idea of how fast the car can accelerates within a period of time to show its thrust and it does travel a streight line to show its stability.

 

[stapel]

I guess one thing you guys left out is why you assumed all these.

What is the "all these" to which you refer? The exercise said to assume constant acceleration, and the straight-line motion is a real-world standard for acceleration measurements of this sort and a standard mathematico-physical simplification. Which other assumptions are you questioning?

Thank you.

Eliz.

 

[morson]

I think sky2rain is not questioning the validity of the assumptions, but rather the point. I think it's important to assume rectillinear motion, in this exercise, even if it may be obvious in some, because as staple said, it makes it a lot simpler.

Also, it's misleading for a manufacturer to describe a vehicle's thrust by describing the acceleration, anyway, as thrust is measured by the resultant force (mass, acceleration).