What is the acceleration of the car

In summary, the conversation discusses a problem involving a car slowing down from 25 m/s to rest in a distance of 75 meters. The question asked for the acceleration of the car. The attempted solution used the equation x = x0 + v0t + 1/2at^2 and resulted in an acceleration of -0.16 m/s^2. Another method using the equation v2 = u2 + 2as resulted in an acceleration of -0.16 m/s^2 as well.
  • #1
colin_delecia
4
0

Homework Statement



A car slows down from 25 to rest in a distance of 75 .
What is the acceleration of the car.

I've been fiddling with this problem pretty much all night but can't seem to get to a correct answer, help would be apprechiated.

Homework Equations



x = x0 + v0t + 1/2at^2
d = 1/2(v0 +v)t

The Attempt at a Solution



x = x0 + v0t + 1/2at^2

75m = (25m/s)(60.5s) + 1/2a(60.5s)^2

75m = 1512.5m + 1/2a(60.5s)(60.5s)
75m = 1512.5m + 1/2a(3660.25s^2)

75m - 1512.5m = 1512.4m - 1512.4m 1/2a(3660.25s^2)
-1437.5m = .5a(3660.25s^2)
------ ----------------

.5 .5


-2875 = a(3660.25s^2)
------ -------------
3660.25 3660.25s^2


-.79m/s2

AND

-25m/s
------
60.5s = -.42m/s2
 
Last edited:
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  • #2


em i don't understand how you got your time? anyway

notice this question doesn't give you time.

so you use the equation of motion that doesn't involve time, which is

v2 = u2 + 2as

now , v2 = 0 , because final car velocity = 0
u2 = 25 as stated in question
s = 75

so 0 = 25 + 2a(75)
a = -25/(2x75) = -0.16

so the negative sign tells you the acceleration is opposite to the direction of the +25 m/s velocity , i.e, the car is decelerating .
 

1. What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction. In simpler terms, it measures how quickly an object is speeding up, slowing down, or changing direction.

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. This can be represented by the equation a = (vf-vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What units is acceleration measured in?

Acceleration is typically measured in meters per second squared (m/s²) in the metric system or feet per second squared (ft/s²) in the imperial system. It can also be measured in other units such as miles per hour squared (mph/s²) or kilometers per hour squared (km/h²).

4. How does acceleration affect an object's motion?

Acceleration directly affects an object's motion by changing its velocity. If an object is accelerating, its speed and/or direction will be changing. This can cause the object to speed up, slow down, or change direction.

5. What factors can affect the acceleration of a car?

The acceleration of a car can be affected by several factors, such as the engine power, weight of the car, aerodynamics, and road conditions. Additionally, external forces such as friction, air resistance, and gravity can also impact the acceleration of a car.

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