How Long Will It Take for a Car to Accelerate from 55 km/h to 75 km/h?

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Homework Help Overview

The discussion revolves around calculating the time it takes for a car to accelerate from 55 km/h to 75 km/h, given its previous acceleration from 35 km/h to 55 km/h. The problem involves concepts of kinematics and dynamics, particularly under the assumption of constant power and neglecting frictional losses.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between initial and final velocities, acceleration, and time. Some suggest using the equation v(t) = v₀ + at directly to find time, while others question the necessity of calculating distance. There is a discussion about the implications of constant power on the acceleration process.

Discussion Status

The conversation is ongoing, with participants sharing different approaches and questioning assumptions about the problem. Some have noted discrepancies in their calculations and are seeking clarification on the dynamics involved, particularly regarding kinetic energy and work done.

Contextual Notes

Participants are working under the assumption of constant power, which affects the acceleration calculations. There is also mention of converting units from km/h to m/s, indicating a potential area of confusion or error in calculations.

Sportsman4920
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If a 1500 kg car can accelerate from 35 km/h to 55 km/h in 3.8 s, how long will it take to accelerate from 55 km/h to 75 km/h? Assume the power stays the same, and neglect frictional losses

what I have tried so far:
55=35+a3.8

a=5.263 km/h squared

75 squared= 55 squared + 2(5.263squared)d

d=46.93

46.93=55+2.6315t
-8.067= 2.6315t

t=3.06 but the answer is obviously wrong
 
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Since acceleration is constant, you can use v(t) = v_{0} + at. Simply apply that formula to the case when v0 = 55 km/h, and v(t) = 75.
 
diodnt they ask you how LONG it takes it takes to reach 75km/h from 55km/h? That means time

you have the initial velocity, you have the final velocity, you have your acceleration, can't you find the time WITHOUT having to find distance?
 
radou said:
Since acceleration is constant, you can use v(t) = v_{0} + at. Simply apply that formula to the case when v0 = 55 km/h, and v(t) = 75.

The question says assume power is constant; since kinetic energy has v^2 in it, it will take longer to up the speed by 20km/h than previously.
 
BerryBoy said:
The question says assume power is constant; since kinetic energy has v^2 in it, it will take longer to up the speed by 20km/h than previously.

You're right. I missed the word 'power'. So it becomes a dynamics problem.
 
Last edited:
when I plug the numbers into the equation 75=55+at

I get 20=5.263t

t=3.8001, but when I plug that in it is wrong. And that would be the same time as it took to get from 35 to 55
??
 
Sportsman4920 said:
when I plug the numbers into the equation 75=55+at

I get 20=5.263t

t=3.8001, but when I plug that in it is wrong. And that would be the same time as it took to get from 35 to 55
??

Again, read BerryBoy's post. As stated, it's a dynamics problem. You have to calculate changes of kinetic energy, which equal the work done. Then plug that work into the equation for power, which, as said, remains constant.

P.S. Convert [km/h] to [m/s].
 
Last edited:

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