Calculating Acceleration of a Braking Train

In summary, the average acceleration of a train traveling at 140 km/h and taking 700m to stop is -1.0802 m/s^2. This was calculated using the kinematic equation (vx)^2=(u)^2 + 2x a x700 m, with an initial velocity of 140 km/h and a final velocity of 0 m/s. This confirms that the correct formula was used.
  • #1
Nanu Nana
95
5

Homework Statement


A train that runs 140 km / h requires about 700m to stop. Calculate the average acceleration of the train while braking.

Homework Equations


v: x/t[/B]

The Attempt at a Solution


v= x/t
so t= x/v= 700m/ (38.89m/s)=18 s
Now to find acceleration a= v/t
a= 38,89m/s / 18s =2,160 m/s^2
They're asking the average so 2,160 m/s2 is our initial acceleration
therefore
0-2,160 m/s^2 / (2) = -1,08024
Is it the correct formula to use ? or is it wrong ?
 
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  • #2
The equation you used for the velocity is correct only if the acceleration is zero (i.e., only if the velocity is constant).
 
  • #3
Oh I see. I think I've found out which kinematic equation to use .

I tried this one
initial velocity = 140 km/h (38,89 m/s)
Final velocity = 0 m/s because its going to stop
(vx)^2=(u)^2 + 2x a x700 m
(38,89)^2=1400 x a
a= -1512,34/ 1400
a= -1,0802
 
  • #4
Nanu Nana said:
Oh I see. I think I've found out which kinematic equation to use .

I tried this one
initial velocity = 140 km/h (38,89 m/s)
Final velocity = 0 m/s because its going to stop
(vx)^2=(u)^2 + 2x a x700 m
(38,89)^2=1400 x a
a= -1512,34/ 1400
a= -1,0802

That's correct. Can you think of a way to confirm that answer is right?
 
  • #5
My workbook says so
 
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1. What is kinematics acceleration?

Kinematics acceleration is the rate of change of an object's velocity over time. It is a vector quantity with both magnitude and direction.

2. How is kinematics acceleration calculated?

Kinematics acceleration can be calculated by dividing the change in an object's velocity by the change in time. The equation for kinematics acceleration is a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What is the difference between kinematics acceleration and angular acceleration?

Kinematics acceleration refers to the change in an object's linear velocity, while angular acceleration refers to the change in an object's rotational velocity. Kinematics acceleration is measured in meters per second squared (m/s²), while angular acceleration is measured in radians per second squared (rad/s²).

4. What is the relationship between kinematics acceleration and force?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that a larger force will result in a larger acceleration, while a larger mass will result in a smaller acceleration.

5. How does kinematics acceleration affect motion?

Kinematics acceleration affects motion by changing the velocity of an object. If the acceleration is positive, the object will speed up in the direction of the acceleration. If the acceleration is negative, the object will slow down in the opposite direction of the acceleration. If the acceleration is zero, the object will maintain a constant velocity.

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