A boxcar of mass 200 tons at rest becomes uncoupled on a 1.5° grade.If the track is considered to be frictionless,what speed does the boxcar have after 10 seconds?
A)0.37 m/s
B)0.59 m/s
C)2.6 m/s
D)4.3 m/s

Question

Quizplus · Accepted Answer

We need to use the equation for the acceleration of an object on an inclined plane without friction: 
a = g*sin(theta), where g is the acceleration due to gravity (9.8 m/s^2) and theta is the angle of the incline (1.5 degrees = 0.02618 radians). 
So, a = 9.8*sin(0.02618) = 0.45 m/s^2. 
Using the equation for displacement, d = (1/2)*a*t^2, where t is the time elapsed (10 s), we can find the distance the boxcar has traveled down the incline: 
d = (1/2)*0.45*(10^2) = 22.5 m 
Now, we can use the equation for final velocity, v = sqrt(2*a*d), to find the speed of the boxcar at the bottom of the incline: 
v = sqrt(2*0.45*22.5) = 2.6 m/s. 
Therefore, our answer is C).

A Boxcar of Mass 200 Tons at Rest Becomes Uncoupled